Answer
$a.\quad 8$
$b.\displaystyle \quad\frac{1}{64}$
$c.\displaystyle \quad\frac{1}{x^{2}}+7$
$d.\displaystyle \quad\frac{1}{(x+7)^{2}}$
Work Step by Step
$(f\circ g)(x)=f[g(x)]=[g(x)]+7$
$=\displaystyle \frac{1}{x^{2}}+7 \qquad ... \quad(c)$
$(f\displaystyle \circ g)(1)=\frac{1}{1^{2}}+7=8 \qquad ... \quad(a)$
$(g\displaystyle \circ f)(x)=g[f(x)]=\frac{1}{[f(x)]^{2}}$
$=\displaystyle \frac{1}{(x+7)^{2}} \qquad ... \quad(d)$
$(g\displaystyle \circ f)(1)=\frac{1}{(1+7)^{2}}=\frac{1}{64} \qquad ... \quad(b)$
