Answer
(a) $\frac{1-a}{a}$
(b) $-\frac{1}{a}$
Work Step by Step
We are given: $g(x)=\frac{1}{x}$; $x=1$, $x=a$
(a) We calculate the net change:
$g(a)-g(1)=\displaystyle \frac{1}{a}-\frac{1}{1}=\frac{1}{a}-\frac{a}{a}=\frac{1-a}{a}$
(b) We calculate the average rate of change:
$\displaystyle \frac{g(a)-g(1)}{a-1}=\frac{\frac{1-a}{a}}{a-1}=\frac{1-a}{a(a-1)}=-\frac{a-1}{a(a-1)}=-\frac{1}{a}$
