DO NOW: Perform the indicated operation.

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DO NOW: Perform the indicated operation. 1.) Find g(f(x)) if f(x) = 2x2 – x and g(x) = 2.) Find g(h(8)) if g(x) = -x2 and h(x) =

Algebra II 5.6: Inverse of a Function

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Example 1 Find the inverse of f (x ) = 3x − 1.

Inverses of Nonlinear Functions In the previous examples, the inverses of the linear functions were also functions. However, this may not always be the case.

Sketch the graph of the inverse relation. Are these inverse functions?

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Example 3 Consider the function f (x ) = 2x 3 + 1. Determine whether the inverse of f is a function (you may use your graphing calculator). Then find the inverse.

Do Now: Solve the literal equation for x. 1. y  3x − 9x 2. a  x − 7xz 3. sx − tx  r 4. C  86x − 59

Example 4

Exploring Inverse Functions Functions f and g are inverses of each other provided: f(g(x)) = x and g(f(x)) = x

Example 5

Practice