MA 113 Study Guide - Final Guide: Intermediate Value Theorem, Function Composition, Inverse Function
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September 20, 2011: each question is followed by space to write your answer. Write your solutions neatly in the space below the question: clearly indicate your answer and the reasoning used to arrive at that answer. Unsup- ported answers may not receive credit: you must give exact answers, rather than decimal approximations. 1: consider the function f (x) = (a) evaluate g(f (1)). Justify your answer. g(f (1)) = g( 1) = ( 1)2 16 = 15. 8 h(x) = (x2 16) 9 x2 25 (x 5)(x + 5) Since division by zero is the only thing we must avoid in this case, the domain of f is given by. D(f ) = {x r : x 6= 5 and x 6= 5} . 3x + 2 (a) if f 1 is the inverse function of f , give a formula for f 1(x). y = 3x + 2 y(3x + 2) = 2x 1.
