Answer
a) $f(f(x))=4x-9$
b) $g(g(x))=-x^4+8x^2-12$
Work Step by Step
We find the composite functions as follows:
a) $f(f(x))=f(2x-3)=2(2x-3)-3=4x-6-3=4x-9$
b) $g(g(x))=g(4-x^2)=4-(4-x^2)^2=4-(16-8x^2+x^4)=-x^4+8x^2-12$
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305115546
ISBN 13:
978-1-30511-554-5
Chapter 2, Functions - Section 2.7 - Combining Functions - 2.7 Exercises - Page 252: 32
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