Chapter 2, Functions - Section 2.7 - Combining Functions - 2.7 Exercises - Page 252: 31

(a) $5-2x^2$ (b) $-4x^{2}+12x-5$

We are given: $f(x)=2x-3$ and $g(x)=4-x^2$ We evaluate: (a) $(f\circ g)(x)=f(g(x))=f(4-x^{2})=2(4-x^{2})-3=8-2x^{2}-3=5-2x^{2}$ (b) $(g\circ f)(x)=g(f(x))=g(2x-3)=4-(2x-3)^{2}=4-(4x^{2}-12x+9)=4-4x^2+12x-9=-4x^{2}+12x-5$