Answers
One way to check if a function is inverse of the other is to take their composition. The composition of two inverse functions will always result in x.
[tex]F(x) = x-2 \\ \\ F^{-1}(x)=x+2 \\ \\ F(F^{-1}(x)) = F(x+2) \\ \\ F(F^{-1}(x)) = (x+2) -2 = x [/tex]
Thus x - 2 and x + 2 are the inverse of each other.
Related Questions
A math club took a test. Twelve of the members had an average score of 80. Eighteen of the members had an average score of 86.
what was the class average score?
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hope tis helps
round 0.246 to the nearest tenth
Answers
You save three-fifths of your paycheck. Which decimal is equivalent to that fraction?
Answers
Answer: 0.6
Step-by-step explanation:
The fractions have the form shown below:
[tex]\frac{a}{b}[/tex]
Where: a is the numerator and b is the denominator.
To convert a fraction to a decimal number, you must divide the numerator by the denominator.
You know that the fraction is three-fifths, which is written as following:
[tex]\frac{3}{5}[/tex]
Therefore, when you divide the numerator 3 by the denominator 5, you obtain the following decimal number which is equivalent to that fraction:
[tex]\frac{3}{5}=0.6[/tex]
Answer:
0.6
Step-by-step explanation:
How can we check the binomial factors to verify that they are truly factors? Are the factors (x + 5)(x – 8) truly factors of x2 – 2x – 30. Show your work.
Answers
a plumber has a 36in. pipe that he has to cut into two pieces so that one piece is 8 in. longer than the other. find the length of each piece?
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and the other one is 14
A cylindrical thermos has a radius of2 in. and is 5 in. high. It holds 10 f oz. To the nearest ounce, how many ounces will a similar thermos with a radius of 3 in. hold? Show your work
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A--------> larger thermos with radius 3 in
B-------> smaller thermos with radius 2 in
we know that
scale factor=radius larger thermos/radius smaller thermos
scale factor=3/2----> 1.5
volume larger thermos=[scale factor]³*volume smaller thermos
volume larger thermos=[1.5]³*10 f oz-----> 3.375*10-----> 33.75 f oz----> 34 f oz
the answer is
34 f oz
what is the limit of f (×) as x approaches - infinty
Answers
So then the limit would be 3/1 = 3.
Alternatively,
[tex]\displaystyle \lim_{x\to\infty}\dfrac{3x^2+6}{x^2-4}=\displaystyle \lim_{x\to\infty}\dfrac{3x^2+6}{x^2-4}\cdot\dfrac{1/x^2}{1/x^2}=\lim_{x\to\infty}\dfrac{3+\frac6{x^2}}{1-\frac4{x^2}} = \dfrac{3+0}{1-0}=\boxed{3}[/tex]
Hope this helps.
Final answer:
The limit of a function as x approaches negative infinity is the value that the function f(x) approaches as x becomes very large in the negative direction. For example, the limit of 1/x is 0 as x approaches negative infinity, while the limit of 1/x² approaches positive infinity. Functions that oscillate, like sin(\u03C0/x), do not have a limit at infinity.
Explanation:
When discussing the limit of a function f(x) as x approaches negative infinity, we are essentially asking what value f(x) gets closer to as x becomes very large and negative. For instance, consider the function 1/x. As x approaches negative infinity, 1/x gets closer to 0, and we say that the limit of 1/x as x approaches negative infinity is 0. Similarly, for a function like 1/x² which "blows up" or increases rapidly as x approaches 0 from either side, we notice that as x approaches negative infinity, the function approaches positive infinity since the squared term always results in a positive number.
However, not all functions have limits at infinity. For functions that oscillate, such as sin(\u03C0/x), as x approaches 0, it oscillates indefinitely between -1 and +1 and does not approach a specific value.
The formal definition of a limit at infinity states: If there is a number L such that f(x) gets arbitrarily close to L when x is sufficiently large (positively or negatively), we write lim f(x) = L as x → -∞.
What shape is the graph of the equation below? (x-5)^2/4^2 + y^2/7^2=1 A. A line B. A circle C. A parabola opening to the right D. A hyperbola opening to the right and left E. A hyperbola opening up and down F. An ellipse
Answers
the answer to your question
is the letter C
Let's explore the equation to see why the graph of the formula that is given sounds like:
((x−5)²/(4)²) + (y²/(7)²) = 1
This equation represents the standard form of an ellipse:
((x−h)²/a²) + ((y-k)²/(b)²) = 1
Where:
*The ellipse's center is (h,k).
*The semi-major axis's length, or horizontal radius, is denoted by a.
*The semi-minor axis's length, or vertical radius, is b.
Comparing the given equation to the standard form, we see that:
*h=5 (center is at x=5)
*a=4 (semi-major axis length)
*b=7 (semi-minor axis length)
Since both a and b are positive and the denominators of both terms are squared, the graph represents an ellipse. Therefore, the correct answer is F. An ellipse.
The given equation is in the form of an ellipse:
((x−5)²/(4)²) + (y²/(7)²) = 1
It matches the standard form of an ellipse equation:
((x−h)²/a²) + ((y-k)²/(b)²) = 1
where (h,k) is the center of the ellipse, and a and b are the lengths of the semi-major and semi-minor axes, respectively.
In this equation, h=5, a=4, and b=7, indicating the ellipse is centered at (5,0) with a horizontal radius of 4 and a vertical radius of 7.
Therefore, the correct answer is F. An ellipse.
Complete Question:
What shape is the graph of the equation below?
A. A line
B. A circle
C. A parabola opening to the right
D. A hyperbola opening to the right and left
E. A hyperbola opening up and down
F. An ellipse
hey can you please help me posted picture of question
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The steps to find the inverse are listed below.
[tex]f(x)= \frac{2x}{7}+4 \\ \\ y= \frac{2x}{7}+4 \\ \\ y-4= \frac{2x}{7} \\ \\ 7(y-4)=2x \\ \\ x= \frac{7(y-4)}{2} \\ \\ f^{-1}(y)= \frac{7(y-4)}{2} \\ \\ f^{-1}(x)= \frac{7(x-4)}{2} \\ \\ [/tex]
Find the value of x for which m//n
A.
31
B.
33
C.
39
D.
41
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180-105 = 75 degrees
Therefore, we match this angle to the given expression.
We have then:
3x-18 = 75
Clearing x we have:
3x = 75 + 18
x = 93/3
x = 31 degrees
Answer:
the value of x is:
A.
31
Form a sequence that has two arithmetic means between -1 and 59.
a.
-1, 29, 29, 59
c.
19, -1, 59, 39
b.
-1, 19, 39, 59
d.
-1, 14, 29, 44, 59
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an = a1 + (n - 1)d
Where:
n = number of figure in the sequence = 4
d = difference between successive number =?
a1 = -1
a4 = 59
Insert the given values into the formula,
59 = -1 + (4 - 1)d
59 = -1 + 3d
59 + 1 = 3d
60 = 3d
d = 60/3 = 20
Therefore, d = 20. This implies that, there is a difference of 20 between successive numbers.
The number sequence is as follow:
-1, 19, 39, 59.
b.-1, 19, 39, 59
which is the coefficient in the algebraic expression 12x + z^4 ?
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Hope this helps!
Simplify the expression. (x1/8 y1/4)2
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Answer:
Step-by-step explanation:
C) x1/4y1/2
This graph shows the solution to the inequalities y>3/2x-2 and y<3/2x-10. Does the system of inequalities have solutions? If so, which region contains the solution?
A) there is no solution
B) there is a solution, and it’s shown by region A.
C) there is a solution, and it’s shown by region C
D) there is a solution, and it’s shown by region B.
Answers
the region A satisfies only the inequality-------> y>3/2x-2
the region C satisfies only the inequality-------> y<3/2x-10
the region B
does not satisfy any of the two inequalities
there is no region that satisfies both inequalities
therefore
the answer is the option
A) there is no solution
Answer:
there is no solution
Step-by-step explanation:
Michelle collects US, Canadian and Mexican stamps. In her collection 80% of the stamps are U.S. and Mexican stamps. there are 3 times as many U.S. stamps as Mexican stamps. WHat percent of Michelle's collections is made up of U.S. stamps?
Answers
The US stamps are 3 times the Mexican stamps. That means that of the 80%, Mexicans comprised of the 20% and US comprised of the 60% to satisfy the relationship of their ratios.
Therefore, 60% of Michelle's collection is made up of US stamps.
Final answer:
Michelle's stamp collection consists of 60% U.S. stamps, determined by solving equations based on the given information that U.S. and Mexican stamps make up 80% of her collection and there are three times as many U.S. stamps as Mexican stamps.
Explanation:
The student asked what percent of Michelle's stamp collection is made up of U.S. stamps if 80% are U.S. and Mexican stamps and there are 3 times as many U.S. stamps as Mexican stamps. To solve this, let's call the percentage of U.S. stamps 'U' and the percentage of Mexican stamps 'M'. According to the given information, U + M = 80%, and U = 3M.
We substitute the second expression into the first to get 3M + M = 80%, which simplifies to 4M = 80%. Dividing both sides by 4 gives M = 20%. As the number of U.S. stamps is three times the number of Mexican stamps, we calculate U as 3 × 20% = 60%. So, the percentage of U.S. stamps in Michelle's collection is 60%.
a student has test scores of 92%, 87%, and 78%. what must she need to score on thenlast test to maintain 80% or better?
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Marisol and Mimi walked the same distance from their school to a shopping mall. Marisol walked 2 miles per hour, while Mimi left an hour later and walked 3 miles per hour. If they reached the mall at the same time how far is the mall from their school?
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The distance walked by Marisol=speed*time=2t
Distance walked by Mimi=3(t-1)
When they've reached school they've all walked the same distance so:
3(t-1)=2t
3t-3=2t
3t-2t=3
t=3
Thus the distance from the mall to their school is 2t=2*3=6 miles
If, in 7 years, Susan will be 2 times as old as she was 3 years ago, what is Susan’s present age? PLEAZE EXPLAIN HOW AND DO IT WITH USING X
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Now, after 7 years ( her age will become 7 +x then) she'll be 2 as old she was 3 years ago.
Her age 3 years ago must be x-3
Now according to question,
twice Her age 3 years ago = her age after 7 years
now,
2(x-3) = 7+x
2x-6 = 7+x
2x-x =7+6
x = 13
x = 13
Therefore, her age presenr age is 13 years.
Answer:
Susan is 13 years old.
Step-by-step explanation:
Susan=x
After 7 years she will be 7+x then she will be 2x as old as she was 3 year ago.
age 3 yrs ago=x-3
2x-6=7+x
if you simplify....
now she is 13
hope it helps!!!!
hey can you please help me posted picture of question
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The correct answer for this completion exercise shown above is the second option (Option B), which is: B. Parent
Therefore, you have:"In each family of function, the parent function is the most basic function in the family"
By definition, the most basic fucntion in each family of functions is called “parent fucntion”. A family of function is a set of function that when you graph them, you can notice that they have common charateristics.
the cost of 10 yearbooks $250 what is the cost of one yearbook
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The cost is x and the amount is 10
So the equation is 10x=$250
Divide 250 by 10 and get 25
$250/10 = $25
_____
Whether you can actually purchase one yearbook for that price depends on a number of factors.
hey can you please help me posted picture of question
Answers
Explanation:
Multiply all the items to get all the possible outcomes (in this case sandwiches).
Kinds of breads = 3
Kinds of meat = 4
Kinds of cheese = 3
Hence 4*3*3 = 36 (Option D)
What is the perimeter of the rectangle? Write your answer in scientific notation. The area is 2.76 x 10 pw12 the width is 4.6 x 10 pw5 pw is the power
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You have
area = 2.76·10^12
width = 4.6·10^5
You want to find the perimeter of the rectangle with these dimensions.
The perimeter of a rectangle is twice the sum of length and width.
perimeter = 2*(length + width)
The length can be figured from the area using the formula for area.
area = length*width
area/width = length . . . . . . . . . divide by width
Filling in the numbers, we have
perimeter = 2*((2.76·10^12)/(4.6·10^5) +(4.6·10^5))
perimeter = 2*(6.0·10^6 +0.46·10^6)
perimeter = 2*6.46·10^6 = 1.292·10^7
The perimeter of the rectangle is ...
1.292·10^7
To calculate the perimeter of a rectangle in scientific notation, divide the given area by the width to find the length, then use the perimeter formula (P = 2×length + 2×width), accounting for the power of 10 in your calculations to maintain proper notation.
Explanation:The perimeter of a rectangle can be found using the formula P = 2×length + 2×width. Given the area of the rectangle (2.76 x 10^12 square units) and the width (4.6 x 10^5 units), we can find the length by dividing the area by the width. The length would therefore be the area divided by the width which is (2.76 x 10^12) / (4.6 x 10^5) = 6 x 10^6 units. Now that we have the length and width, we can calculate the perimeter by substituting into the formula: P = 2×(6 x 10^6) + 2×(4.6 x 10^5) = 1.2 x 10^7 + 9.2 x 10^5. Converting the width to the same power of 10, we get P = 1.2 x 10^7 + 0.092 x 10^7 = 1.292 x 10^7 units. This expresses the perimeter in scientific notation.
Rex painting the garage in the shed he uses 3 gallons of paint on the garage he uses 3/4 of that amount on the shed enter the amount of paint in gallons Rex uses on the shed
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0.75×(3 gallons) = 2.25 gallons
Rex uses 2.25 gallons of paint on the shed.
Rex uses 2.25 gallons of paint on the shed, which is [tex]\( \frac{3}{4} \)[/tex] of the 3 gallons of paint he uses on the garage.
To find out how much paint Rex uses on the shed, we need to calculate [tex]\( \frac{3}{4} \)[/tex] of the amount of paint he uses on the garage.
Rex uses 3 gallons of paint on the garage.
Therefore, the amount of paint he uses on the shed is:
Paint used on the shed = [tex]\frac{3}{4} \times 3[/tex]
Calculating this:
Paint used on the shed = [tex]\frac{3 \times 3}{4}[/tex]
= [tex]\frac{9}{4}[/tex]
= 2.25
So, Rex uses 2.25 gallons of paint on the shed.
What are the dimensions of the image at fraction 1 over 2 times its current size?
Length = 4 inches, width = 5 inches
Length = 6 inches, width = 8 inches
Length = 10 inches, width = 12 inches
Length = 16 inches, width = 20 inches
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Answer:
Length = 4 inches, width = 5 inches
Step-by-step explanation:
you have $120 to donate equally to several charities. Does this situaton represent direct or inverse variation? Explain.
Answers
The difference between direct and inverse variation is in direct variation, as one variable goes up the other does too, while in inverse, as one variable goes up the other falls.
In this case, as you donate to more charities, the amount you donate to each charity falls, because you donate an equal amount. This means it's inverse variation.
Hope this helps!
Use complete sentences to describe the domain of the cosine function.
Answers
The cosine function takes x values from all real numbers.
Therefore, the domain of the cosine function is a real numbers.
hey can you please help me posted picture of question
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( 6 - 2i) + ( 11 + 6i)
= 6 + 11 - 2i + 6i
= 17 + 4i
So the answer to this question is option D
[tex]42 \times 42 \times 29 = [/tex]
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Hope this helps :)
y equals x + z + 5 Z equals -3 y - 3 2x minus y equals negative 4 How can i solve using 3 variable systems of equation
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If you have
x +z +5z = -3y -3
3x -y = -4
Then you can rewrite as
x = -1.5 -0.6z
y = -0.5 -1.8z
_____
You can get this by any of the usual methods of solving linear equations. Just treat the system as two equations in x and y with the z terms on the right side of the equal sign:
x +3y = -3 -6z
3x -y = -4
Which of the following is another way to express the equation 16 = -9 + z?
A.16 = z - 9
B.16 = z + 9
C.16 = -z + 9
D.16 = -z - 9
Answers
Answer:
16 = z - 9
Step-by-step explanation:
I did the same problem and answered this, 16 = z - 9. It was correct.