1 7 Inverse Relations and Functions Example 1

Example 1: Determine if the function has an inverse that exists a. f (x)

Example 2: Determine whether f has an inverse function for. If it does, find

Example 3: Determine whether f has an inverse function for. If it does, find

Example 4: Determine whether f has an inverse function for. If it does, find

Compositions of Inverse Functions: Two functions, f and g, are inverses functions if and

Example 5: Show that f (x) = x 2 – 2, x 0 and

Example 6: Use the graph of relation A to sketch the graph of its

Example 7: How can we use the graph of the function to graph its

Example 8: The fixed costs for manufacturing one type of stereo system are $96,

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1. 7 – Inverse Relations and Functions

Example 1: Determine if the function has an inverse that exists a. f (x) = 4 x 2 + 4 x + 1 b.

Finding an Inverse:

Example 2: Determine whether f has an inverse function for. If it does, find the inverse function and state any restrictions on its domain.

Example 3: Determine whether f has an inverse function for. If it does, find the inverse function and state any restrictions on its domain.

Example 4: Determine whether f has an inverse function for. If it does, find the inverse function and state any restrictions on its domain.

Compositions of Inverse Functions: Two functions, f and g, are inverses functions if and only if: Ø f(g(x)) = x for every x in the domain of g(x) and Ø g(f(x)) = x for every x in the domain of f(x).

Example 5:

Example 5: Show that f (x) = x 2 – 2, x 0 and are inverses of each other.

Example 6: Use the graph of relation A to sketch the graph of its inverse.

Example 7: How can we use the graph of the function to graph its inverse Function?

Example 8: The fixed costs for manufacturing one type of stereo system are $96, 000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f(x) = 96, 000 + 80 x. a. Explain why the inverse function f – 1(x) exists. Then find f – 1(x).

Example 8: The fixed costs for manufacturing one type of stereo system are $96, 000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f(x) = 96, 000 + 80 x. b. What do f – 1(x) and x represent in the inverse function?

Example 8: The fixed costs for manufacturing one type of stereo system are $96, 000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f(x) = 96, 000 + 80 x. c. What restrictions, if any, should be placed on the domain of f (x) and f – 1(x)? Explain.

Example 8: The fixed costs for manufacturing one type of stereo system are $96, 000 with variable cost of $80 per unit. The total cost f (x) of making x stereos is given by f(x) = 96, 000 + 80 x. d. Find the number of stereos made if the total cost was $216, 000.