$U$ is a continuous random variable $R.V$ uniformly distributed over $[-2, 3]$. Let $R.V$ $G=U^2$. Find $f_G(g)$

Question

Please help me in verifying whether have I solved the following problem correctly or not. If no kindly guide me.

Let $U$ is a continuous random variable $R.V$ uniformly distributed over $[-2, 3]$.
Define new $R.V$

$G=U^2$

find $f_G(g)$

My attempt:

$f_U(u) = 0.2$

$F_U(u)= 0.2U$

Now we have:

$F_G(g) = Pr(G<=g) = Pr(U^2<=g)=Pr(\sqrt{-g}<U<\sqrt{g})= F_U(\sqrt{g})-F_U(\sqrt{-g})= 2/5*(\sqrt{g})$

Hence : $f_G(g) = 2/(10*\sqrt{g})$

Answer 1

$G$ takes values in $(0,9)$. $P(U^{2}\leq g)=P(-2,<U<3, -\sqrt g \leq U \leq \sqrt g)$. This is $\frac 2 5 \sqrt g$ only when $0 <g <4$. For $4<g<9$ we get $\frac 1 5 (2+\sqrt g)$. Now differentiate.