# Chapter 4 - Calculating the Derivative - 4.3 The Chain Rule - 4.3 Exercises - Page 225: 11

$f[g(x)]=\sqrt{8x^{2}-4}$ $g[f(x)]=8x+10$

#### Work Step by Step

In the expression for f(x), replace x with g(x) $f[g(x)]=\sqrt{g(x)+2}$ $=\sqrt{(8x^{2}-6)+2}$ $=\sqrt{8x^{2}-4}$ In the expression for g(x), replace x with f(x) $g[f(x)]=8(f(x))^{2}-6$ $=8(\sqrt{x+2})^{2}-6$ $=8x+16-6$ $=8x+10$

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