University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.2 - Combining Functions; Shifting and Scaling Graphs - Exercises - Page 18: 5


$a. 2$ $b. 22$ $c. x^2+2$ $d. x^2+10x+22$ $e. 5$ $f. -2$ $g. x+10$ $h. x^4-6x^2+6$

Work Step by Step

$f(x)=x+5$ $g(x)=x^2-3$ $a.\quad f(g(0))=?$ $f(g(x))=(x^2-3)+5=x^2+2$ $f(g(0))=0^2+2=2$ $b.\quad g(f(0))=?$ $g(f(x))=(x+5)^2-3=x^2+10x+25-3$ $g(f(0))=22$ $c.\quad f(g(x))=x^2+2$ $d.\quad g(f(x))=x^2+10x+22$ $e.\quad f(f(-5))=?$ $f(f(x))=(x+5)+5=x+10$ $f(f(-5))=-5+10=5$ $f.\quad g(g(2))=?$ $g(g(x))=(x^2-3)^2-3=x^4-6x^2+9-3$ $=x^4-6x^2+6$ $g(g(2))=2^4-6(2)^2+6=16-24+6$ $=-2$ $g.\quad f(f(x))=x+10$ $h.\quad g(g(x))=x^4-6x^2+6$
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