Chapter 12 - Exponential Functions and Logarithmic Functions - 12.1 Composite Functions and Inverse Functions - 12.1 Exercise Set - Page 787: 10

$a.\quad 0$ $b.\quad 20$ $c.\quad x^{2}-1$ $d.\quad x^{2}+8x+11$

$(f\circ g)(x)=f[g(x)]=[g(x)]+4$ $=x^{2}-5+4$ $=x^{2}-1 \qquad ... \quad(c)$ $(f\circ g)(1)=1^{2}-1=0 \qquad ... \quad(a)$ $(g\circ f)(x)=g[f(x)]=[f(x)]^{2}-5$ $=(x+4)^{2}-5$ $=x^{2}+8x+16-5$ $=x^{2}+8x+11 \qquad ... \quad(d)$ $(g\circ f)(1)=1^{2}+8(1)+11=20 \qquad ... \quad(b)$