Inverse Functions with mathisfun.com

Multiple Choice

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

Multiple Choice

How is the inverse of a function usually denoted?

• f(x) + 1

• f(x) / 1

• f⁻¹(x)

• f(x) - 1

Multiple Choice

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

Multiple Choice

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

Multiple Choice

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

• 2

• 4

• 11

• 8

Multiple Choice

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

• 2

• 4

• 11

• 8

Multiple Choice

What is the final form of the inverse function f⁻¹(x) for the function f(x) = 2x + 3?

• f⁻¹(x) = (x - 3)/2

• f⁻¹(x) = (x + 3)/2

• f⁻¹(x) = (x/2) + 3

• f⁻¹(x) = 2x - 3

Multiple Choice

What is the inverse of multiplication?

• Division

• Addition

• Subtraction

• Exponentiation

Multiple Choice

What is the inverse function of e^x?

• ln(y)

• log_{10}(y)

• e^y

• x^e

Multiple Choice

What should you be careful about when finding the inverse of the function 1/x?

• x and y not zero

• x and y are zero

• x and y are negative

• x and y are positive

Multiple Choice

What is the inverse function of a^x?

• log_a(y)

• ln(y)

• a^y

• x^a

Multiple Choice

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

• Because it only works with positive numbers

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

• Because its domain is restricted to x ≥ 0

• Because it cannot be graphed

Multiple Choice

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

• By using only positive numbers

• By using only negative numbers

• By restricting the domain to x ≥ 0

• By squaring only even numbers

Multiple Choice

What is necessary for a function to have an inverse?

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

• The function must pass the vertical line test

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

• The function must be a linear function

Multiple Choice

What is the domain 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.

Multiple Choice

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.

Multiple Choice

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.

Multiple Choice

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

• Extend the domain to include all real numbers.

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

• Make the domain equal to the range.

• Nothing, the function already has an inverse.

Multiple Choice

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.

Multiple Choice

What are the graphs of f(x) and f^(-1)(x) symmetric across?

• The line y = x

• The line y = -x

• The x-axis

• The y-axis

Multiple Choice

When the domain is restricted to x ≥ 0, what is the function of the square root of x?

• f(x) = √x

• f(x) = x^2

• f(x) = -√x

• f(x) = -x^2

Multiple Choice

Which of the following statements is true for the function f(x) = x^2 when x ≥ 0?

• It is the square of x for x less than or equal to zero.

• It is the square root of x for x greater than or equal to zero.

• It is the square of x for x greater than or equal to zero.

• It is the inverse of the square root of x for x less than or equal to zero.

Multiple Choice

What is the relationship between the functions f(x) = x^2 for x ≥ 0 and f(x) = √x for x ≥ 0?

• They are inverses of each other.

• They are the same function.

• They are unrelated functions.

• One is the derivative of the other.