Chapter 12 - Exponential Functions and Logarithmic Functions - 12.1 Composite Functions and Inverse Functions - 12.1 Exercise Set - Page 787: 14

$a.\quad 1/9$ $b.\quad 3$ $c.\displaystyle \quad\frac{1}{(x+2)^{2}}$ $d.\displaystyle \quad \frac{1}{x^{2}}+2$

$(f\displaystyle \circ g)(x)=f[g(x)]=\frac{1}{[g(x)]^{2}}$ $= \displaystyle \frac{1}{(x+2)^{2}} \qquad ... \quad(c)$ $(f\displaystyle \circ g)(1)=\frac{1}{(1+2)^{2}}=\frac{1}{9} \qquad ... \quad(a)$ $(g\circ f)(x)=g[f(x)]=[f(x)]+2$ $= \displaystyle \frac{1}{x^{2}}+2 \qquad ... \quad(d)$ $(g\displaystyle \circ f)(1)=\frac{1}{(1)^{2}}+2=3 \qquad ... \quad(b)$