Lesson 7.1 Inverse functions and Function Composition

Last updated over 1 year ago

14 questions

Note from the author:

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

Instructions

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

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Rock Skipping

Paper Sales

Space Again Again

Strictly Algebra

Lesson 7.1 Inverse functions and Function Composition

Last updated over 1 year ago

14 questions

Note from the author:

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

Instructions

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

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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.

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.

Rock Skipping

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?

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.

Paper Sales

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.

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.

Space Again Again

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.

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

Strictly Algebra

Lesson 7.1 Inverse functions and Function Composition

Lesson 7.1 Inverse functions and Function Composition

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.

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.

Lesson 7.1 Inverse functions and Function Composition

Lesson 7.1 Inverse functions and Function Composition

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.

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.

Find
of the following functions.

Find
of the following functions.

Find
of the following functions.

Find
of the following functions.