Lesson 7.1 Inverse functions and Function Composition

Instructions

I can find the inverse of a function and use composition of functions to verify inverse functions.

A clothing store is having a “40% off everything” sale. Ted has a $25 gift card. The function 
represents Ted’s cost T (in dollars) for items that cost cdollars. The function 
represents the purchase price P (in dollars) for items that originally cost c dollars.

2

Use the information from the problem above to write Ted’s cost T as a function of the purchase cost P.

2

Now, use the function to find Ted’s cost when the original cost of his items is $54.

2

Write a function that applies the gift card first and then the discount?

3

Should he ask for the gift card to be applied before or after a discount? Explain.

A small rock is thrown into a pool from the shore, creating ripples in the water. The ripples form concentric circles. The function r(t) = 14t models the radius (in inches) of the outer ripple t seconds after the rock enters the water. Write a function for the area (in square inches) of the outer ripple as a function of time (in seconds). What is the approximate area of the circle defined by the outer ripple 6 seconds after the rock was dropped?

3

A small rock is thrown into a pool from the shore, creating ripples in the water. The ripples form concentric circles. The function r(t) = 14t models the radius (in inches) of the outer ripple t seconds after the rock enters the water. Write a function for the area (in square inches) of the outer ripple as a function of time (in seconds). What is the approximate area of the circle defined by the outer ripple 6 seconds after the rock was dropped? Round to the nearest whole square inch.

Sally earns a weekly salary of $800 plus a 5% commission from her weekly sales. The function 
models Sally’s total weekly earnings when her weekly sales are s dollars.

2

What is the inverse function of E(s)?

2

Describe the domain and range of s(E), the inverse, in the context of the situation.

2

Determine Sally’s weekly sales when she earns a total of $2000 for the week.

The overall distance between the moon and Earth is  changing because the moon is pulling away from us.  The function 
gives the time T (in millions of years) from now that the moon will be D (in kilometers) from Earth.

3

How far will the moon be from Earth in 1000 million years from now?

2

Find
of the following functions.

2

Find
of the following functions.

3

Find
of the following functions.

3

Find
of the following functions.

2

Use the information from the problem above to write Ted’s cost T as a function of the purchase cost P.

Now, use the function to find Ted’s cost when the original cost of his items is $54.

Write a function that applies the gift card first and then the discount?

Should he ask for the gift card to be applied before or after a discount? Explain.

What is the inverse function of E(s)?

Describe the domain and range of s(E), the inverse, in the context of the situation.

Determine Sally’s weekly sales when she earns a total of $2000 for the week.

How far will the moon be from Earth in 1000 million years from now?

Find of the following functions.

Find of the following functions.

Find of the following functions.

Find of the following functions.

Find the inverse of the following function.

Find
of the following functions.

Find
of the following functions.

Find
of the following functions.

Find
of the following functions.