I am having a fair bit of trouble with combinations of functions.

First, I'd just like confirmation on whether or not I done a more basic question correctly.

1.) If $\displaystyle f(x)=x^2 -x -2, g(x)= x - 3 $ ,and$\displaystyle h(x) =2x $ determine the following:

b.) $\displaystyle f(h(g(0)))$

So

$\displaystyle g(0)=0-3$

$\displaystyle g(0)=-3$

$\displaystyle h(g(0))=2(-3)$

$\displaystyle h(g(0))=-6$

$\displaystyle f(h(g(0)))=f(-6)$

$\displaystyle f(h(g(0)))=(-6)^2 -(-6) -2$

$\displaystyle f(h(g(0)))=40$

Is this correct?

For the next question I am given the following:

I don't know how I am supposed to use the graph to evaluate each expression here. Also, is the expression for a.) the same thing as $\displaystyle f(g(2))$?

Lastly I am asked:

If $\displaystyle f(x)=x^2 -x +2 $ and $\displaystyle g(x)=x-2$, find $\displaystyle h(x) $ such that $\displaystyle f(x)=g(h(x))$.

I have no idea how to solve this one.