Answer
a. $f(0)=0$
$f(2)=\frac{\sqrt 2}{3}$
$f(a+2)=\frac{\sqrt a+2}{a+3}$
b. The domain is $D=(0,\infty)$ except $-1$
c. Average rate of change $=\frac{24\sqrt 10-88\sqrt 2}{33}$0.
Work Step by Step
We are given $f(x)=\frac{\sqrt x}{x+1}$
a. $f(0)=\frac{\sqrt 0}{0+1}=0$
$f(2)=\frac{\sqrt 2}{2+1}=\frac{\sqrt 2}{3}$
$f(a+2)=\frac{\sqrt a+2}{a+2+1}=\frac{\sqrt a+2}{a+3}$
b. Find the domain of f
$x\geq0$
$x+1\ne0$
$x\ne-1$
The domain is $D=(0,+\infty)$ except $-1$
c. Net change: $f(10)-f(2)=\frac{\sqrt 10}{11}-\frac{\sqrt 2}{3}=\frac{3\sqrt 10-11\sqrt 2}{33}$
Average rate of change =$\frac{f(10)-f(2)}{10-2}=\frac{\frac{3\sqrt 10-11\sqrt 2}{33}}{8}=\frac{24\sqrt 10-88\sqrt 2}{33}$
