A few days ago

Question on functions?

I need help understanding this math concept! its only one question so don’t worry about “doing my homework for me.” here is the question:

Show that for each pair of function, g and h,

g(h(x)) = x for all x in the domain g(h(x))

and h(g(x)) = x for all x in the domain h(g(x))

#1. g(x) = (-2/3)(x+1) h(x) = (-3/2)(x)-1

thank you so much for your help =D

Top 4 Answers
A few days ago

Favorite Answer

I am doing this too…

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!!!


A few days ago
OK, let’s start with a simple example, if I told you f(x) = x^2 and then told you to show me that f(2) =4 what would you do? you would replace x with whatever is in the parenthesis.. same concept..

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!!


A few days ago
show that g(h(x)) = h(g(x)).

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).


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

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A few days ago
g(h(x)) = (-2/3)((-3/2)(x-1)+1))

-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))