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

$F(x)=f\circ g(x)$ for $g(x)=\cos x,\qquad f(x)=x^{2}$

$f\circ g(x)=f[g(x)]$ Rule of thumb: Ask yourself what would be the last operation if you used a calculator, step by step? (Answer: Square the current result) $f(x)=x^{2}$ $ F(x)=f(\cos x)$ So, if $g(x)=\cos x$ and $f(x)=x^{2}$ then $F(x)=f\circ g(x)$