Inverse function

Question

It is given that x = 7-h(x)/3-h(x), where h(x) ≠ 0, find h-¹ (2).

Answer 1

Solve for h(x) then determine h(2)

Answer 2

Just to add on to Mark's answer a bit, it appears you have are starting with what is typically the second step of an inverse function problem in which you swap x with h(x). You may find it easier to substitute y for h(x) and solve for that instead as a placeholder. That is to say instead of what you start with use this:

x = (7-y)/(3-y)

*multiply both sides by (3-y) to get rid of the fraction*

x(3-y)=7-y

*Distribute*

3x-3y = 7-y

*Get our y term on one side and x on the other*

-2y = -3x + 7

*Divide by -2 to get y alone*

y = (3/2)x - 7/2

*swap back in h^-1(x) for y*

h^-1(x) = (3/2)x - 7/2

Now plug in 2 for x as Mark suggests.