Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 11 - Cumulative Review: 24b

Answer

$(f\circ g)(x) = x^2+2x-1 ,\\ (g\circ f)(x) = x^2-1 $

Work Step by Step

With $f(x)=x^2-2$ and $g(x)=x+1$, then, \begin{array}{l} (f\circ g)(x) \\= f(g(x)) \\= f(x+1) \\= (x+1)^2-2 \\= x^2+2x+1-2 \\= x^2+2x-1 ,\\\\ (g\circ f)(x) \\= g(f(x)) \\= g(x^2-2) \\= x^2-2+1 \\= x^2-1 .\end{array}
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