I believe they are wanting you to show that both g(h(x)) and h(g(x)) both equal x which means they are inverses of each other. So basically solve the problem and your answer for both functions should be x.

Good Luck!!!

So, for yours g(h(x)) you are replacing h(x) into the g(x) equations.. resulting in: g(-3/2x -1)= -2/3((-3/2x -1) +1)

g(-3/2x -1)= x -1 +1 which does equal x

Now do the same for h(g(x)) replace g(x) into the h(x) equation. I already checked and it does equal 1, if you get stuck on that one, email me!!

g(h(x)) = (-2/3){[(-3/2)x – 1] + 1}

substituting h(x) to x in g(x).

h(g(x)) = {(-3/2)[(-2/3)(x + 1)] – 1}

substituting g(x) to x in h(x).

hence,

g(h(x)) = x = h(g(x))

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-2/3(-3/2) = 1

-1 + 1 = 0

so.. g(h(x)) = 1x = x

It’s the same for h(g(x)) and I have no idea wtf the domain part is about, but its probably having to do with the fact g(h(x)) = h(g(x))