What analogy is used in the image to explain the concept of a function and its inverse?

An apple turning into a banana and back

A cat turning into a dog and back

A book turning into a movie and back

Water turning into ice and back

What is the reason the square function does not have an inverse as it stands?

Because it can have two different x-values for one y-value

Because it only works with positive numbers

Because its domain is restricted to x ≥ 0

How can we fix the issue of the square function not having an inverse?

By restricting the domain to x ≥ 0

What is necessary for a function to have an inverse?

The function must have unique x-values for each y-value

The function must have unique y-values for each x-value

The function must pass the vertical line test

The function must be a linear function

What is required for a function to have an inverse?

The function must be bijective.

The function must be continuous.

The function must be differentiable.

The function must be integrable.

What does it mean for a function to be bijective?

The function has exactly one x-value for every y-value and vice versa.

The function has a repeated x-value for a single y-value.

The function has a repeated y-value for a single x-value.

The function has no x-values or y-values.

What is the domain of a function?

The set of all possible inputs to the function.

The set of all possible outputs of the function.

The set of all x-values that the function maps to y-values.

The set of all y-values that the function maps to x-values.

What is the range of a function?

The set of all possible outputs of the function.

The set of all possible inputs to the function.

The set of all x-values that the function maps to y-values.

The set of all y-values that the function maps to x-values.

Why might one need to "restrict the domain" of a function?

To ensure the function has an inverse.

To make the function continuous.

To make the function differentiable.

To make the function integrable.

Why does the function f(x) as initially shown not have an inverse?

Because some y-values will have more than one x-value.

Because it has a restricted domain.

Because it is a linear function.

What must be done to the domain of the function f(x) to allow it to have an inverse?

Restrict the domain so there is a unique x for every y.

Extend the domain to include all real numbers.

Make the domain equal to the range.

Nothing, the function already has an inverse.

What is the relationship between a function and its inverse in terms of domain and range?

The function goes from the domain to the range, and the inverse goes from the range back to the domain.

The function and its inverse have the same domain and range.

The function goes from the range to the domain, and the inverse goes from the domain to the range.

There is no relationship between the domain and range of a function and its inverse.

When plotting the function f(x) and its inverse f^{-1}(x), how should they be labeled to correctly represent the inverse relationship?

Both should be plotted in terms of x.

Both should be plotted in terms of y.

f(x) should be plotted in terms of x and f^{-1}(x) in terms of y.

f(x) should be plotted in terms of y and f^{-1}(x) in terms of x.

Why is it not possible to find an inverse for the function f(x) = x/2 + sin(x)?

Because we cannot solve for "x"

Because it is a linear function

What is NOT true about the notation f^{-1}(x)?

It represents the inverse of the function f

What might be necessary to do when finding an inverse of a function?

Restrict the domain of the function

Ignore the domain of the function

Inverse Functions

Authored by Juan Anton

Mathematics

12th Grade

41 Questions

CCSS covered

Used 2+ times

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the inverse function of f(x) = 2x + 3?

f⁻¹(x) = (x - 3) / 2

f⁻¹(x) = (x + 3) / 2

f⁻¹(x) = 2x - 3

f⁻¹(x) = (3 - x) / 2

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the inverse of a function usually denoted?

f(x) + 1

f(x) / 1

f⁻¹(x)

f(x) - 1

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step to find the inverse of the function f(x) = 2x + 3?

Add 3 to x

Divide x by 2

Subtract 3 from y

Multiply x by 2

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the second step to find the inverse of the function f(x) = 2x + 3 after subtracting 3 from y?

Add 3 to y

Divide y by 2

Multiply y by 2

Subtract 2 from y

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of applying the inverse function f^-1 to the value of the function f(4)?

Tags

CCSS.HSF-BF.B.4C

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If f(x) = 2x + 3 and f^-1(x) = (x - 3)/2, what is f^-1( f(4) )?

Tags

CCSS.HSF-BF.B.4B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

According to the image, what is the relationship between a function f and its inverse f^-1 when applied in sequence?

f^-1( f(x) ) = x

f^-1( f(x) ) = 2x

f( f^-1(x) ) = x + 3

f( f^-1(x) ) = 2x + 3

Tags

CCSS.HSF-BF.B.4B

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Inverse Functions

What is the inverse function of f(x) = 2x + 3?

How is the inverse of a function usually denoted?

What is the first step to find the inverse of the function f(x) = 2x + 3?

What is the second step to find the inverse of the function f(x) = 2x + 3 after subtracting 3 from y?

What is the result of applying the inverse function f^-1 to the value of the function f(4)?

If f(x) = 2x + 3 and f^-1(x) = (x - 3)/2, what is f^-1( f(4) )?

According to the image, what is the relationship between a function f and its inverse f^-1 when applied in sequence?

What analogy is used in the image to explain the concept of a function and its inverse?

What is the first step in finding the inverse of the function f(x) = 2x + 3 using algebra?

After replacing f(x) with y and subtracting 3 from both sides, what is the resulting equation?

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