Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 44: 43

$F(x)=f\circ g(x)$ for $g(x)=2x+x^{2},\qquad f(x)=x^{4}$

$f\circ g(x)=f[g(x)]$ Rule of thumb: Ask yourself what would be the last operation if you used a calculator, step by step? (Answer: Raise to the 4th power) $f(x)=x^{4}$ $F(x)=f(2x+x^{2})$ So, if $g(x)=2x+x^{2}$ and $f(x)=x^{4}$ then $F(x)=f\circ g(x)$ $g(x)=2x+x^{2},\qquad f(x)=x^{4}$