Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.7 - Combining Functions - 2.7 Exercises - Page 217: 49

Answer

$f\circ g(x)=(x+1)^{2};\qquad $ domain: all reals, $(-\infty,\infty)$ $ g\circ f(x)=x^{2}+1; \quad$ domain: all reals, $(-\infty,\infty)$ $ f\circ f(x)=x^{4} ;\quad$ domain: all reals, $(-\infty,\infty)$ $ g\circ g(x)=x+2; \quad$ domain: all reals, $(-\infty,\infty)$

Work Step by Step

f(x) is defined for all x, g(x) is defined for all x $f\circ g(x)=f[g(x)]=[g(x)]^{2}$ $=(x+1)^{2};\qquad $ domain: all reals, $(-\infty,\infty)$ $g\circ f(x)=g[f(x)]=f(x)=1$ $=x^{2}+1; \quad$ domain: all reals, $(-\infty,\infty)$ $f\circ f(x)=f[f(x)]==[f(x)]^{2}$ $=(x^{2})^{2}$ $=x^{4} ;\quad$ domain: all reals, $(-\infty,\infty)$ $g\circ g(x)=g[g(x)]=g(x)+1$ $=(x+1)+1$ $=x+2; \quad$ domain: all reals, $(-\infty,\infty)$
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