Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 44: 36


(a) $$f(g(x)) = sin(x^2+1)$$ $$(-\infty, \infty)$$ (b) $$g(f(x)) = sin^2x+1$$ $$(-\infty, \infty)$$ (c) $$f(f(x)) = sin(sinx)$$ $$(-\infty, \infty)$$ (d) $$g(g(x)) =x^4+2x^2+2$$ $$(-\infty, \infty)$$

Work Step by Step

$f(x)=sinx$ $g(x)=x^2+1$ (a) $f(g(x)) = sin(x^2+1)$ We have no restrictions, so the domain is: $(-\infty, \infty)$ (b) $g(f(x)) = sin^2x+1$ Same here, no restrictions. The domain is: $(-\infty, \infty)$ (c) $f(f(x)) = sin(sinx)$ No restrictions. The domain is: $(-\infty, \infty)$ (d) $g(g(x)) = (x^2+1)^2+1 = x^4+2x^2+1+1 = x^4+2x^2+2$ No restrictions. The domain is: $(-\infty, \infty)$
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