For each pair of functions, find f(g(x))

Property of InversesIf f and f ­1 are inverses, then f(a) = b if and only if f ­1 (b) = a.ex. Let f(x) ­ x ­ 4 and represent its inverse as f ­1 (x) = x + 4.Evaluate f(6). Evaluate f ­1 (2).Because f(x) and f ­1 (x) are inverses, f(6) = 2 and f ­1 (2) = 6.When the inverse of a function is a function, the original function isone­to­one. Recall that the vertical line test can be used to determinewhether a relation is a function. Similarly, the horizontal line test can beused to determine whether the inverse of a function is also a function.3

Ex. 2 Find the inverse of each function. Then graph the function andits inverse.a. f(x) = 2x ­ 5b. f(x) = x 2 + 14

Verifying Inverses You can determine whether two functions areinverses by finding both of their compositions. If both compositionsequal the identity function I(x) = x, then the functions are inversefunctions.Ex. 3 Determine whether each pair of functions are inverse functions.Explain your reasoning.a. f(x) = 3x + 9 and g(x) = 1/3x ­ 3b. f(x) = 4x 2 and g(x) = 2√x5

ASSN: p. 420, 421 9,11,15,17,19,21,23,27,29,31,37,39,43,45Review p. 422 57­75 odd6