Answer
(a) $g(0)=-\frac{1}{2}$
(b) $t=-1$
Work Step by Step
(a) Use $t=0$ to get $g(0)=\frac{1}{0+2}-1=\frac{1}{2}-1=\frac{1}{2}-\frac{2}{2}=-\frac{1}{2}$.
(b) Use the fact that $g(t)=0$ for some $t$ to get $$\frac{1}{t+2}-1=0$$ Add $1$ to both sides to get $$\frac{1}{t+2}=1$$ Multiply both sides of the equation by $t+2$ to get $1=1(t+2)=t+2$. Finally, subtract $2$ from each side to get $$t=1-2=-1$$.
