Question

Pre cal show algebraically that f and g are inverse function. f(x)=2x+3;g(x)=x-3/2

Answer 1

You need to isolate x. Lets say you write f(x) as y. Then you have:\[y=2x+3\] now you isolate x in this function, and then you should get: \[x=y-3/2\] Now you swap around x and y, this gives you the inverse function.

Answer 2

A couple additions:
it's so hard to do math with text only!
You meant g(x) = (x-3)/2 , not g(x) = x-3/2 (they're different).
Ditto with x = (y-3)/2, not x = y - 3/2

In precalc, what the teacher/author might be wanting you to do is to verify that
f(g(x) = x ( or, g(f(x) = x )