2.8

Topic

Inverse Functions

Practice by unit: Exponential and Logarithmic Functions

Sub-standards

• 2.8.A.1 — Determine the input-output pairs of the inverse of a function. On a specified domain, a function, f , has an inverse function, or is invertible, if each output value of f is mapped from a unique input value. The domain of a function may be restricted in many ways to make the function invertible.
• 2.8.B.1 — Determine the inverse of a function on an invertible domain. The composition of a function, f , and its inverse function, f −1 , is the identity function; that is, f f ( −1 (x)) = f −1( f x( )) = x.
• 2.8.B.2 — On a function’s invertible domain, the function’s range and domain are the inverse function’s domain and range, respectively. The inverse of the table of values of y = f (x) can be found by reversing the input-output pairs; that is, (a b, ) corresponds to (b a, ). continued on next page UNIT 2
• 2.8.B.3 — Determine the inverse of a function on an invertible domain. The inverse of the graph of the function y = f (x) can be found by reversing the roles of the x- and y-axes; that is, by reflecting the graph of the function over the graph of the identity function h(x) = x.
• 2.8.B.4 — The inverse of the function can be found by determining the inverse operations to reverse the mapping. One method for finding the inverse of the function f is reversing the roles of x and y in the equation y = f (x), then solving for f − y = 1 (x).
• 2.8.B.5 — In addition to limiting the domain of a function to obtain an inverse function, contextual restrictions may also limit the applicability of an inverse function. UNIT 2 Required Course Content