Inverse Functions

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

How is the inverse of a function usually denoted?

• f(x) + 1

• f(x) / 1

• f⁻¹(x)

• f(x) - 1

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

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

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

• 2

• 4

• 11

• 8

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

• 2

• 4

• 11

• 8

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

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

• A cat turning into a dog and back

• A book turning into a movie and back

• An apple turning into a banana and back

• Water turning into ice and back

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

• Subtract 3 from both sides

• Divide both sides by 2

• Swap sides

• Put "y" for "f(x)"

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

• y = 2x

• y - 3 = 2x

• y/2 = x

• y - 3 = x