How do you verify inverses?

Question

the question is y=3x-3...
we know how to make an inverse but how do you verify it using composition?

Answer 1

one way is to check to make sure that

f(f ^-1(x)) = x
and
f ^-1(f(x)) = x

For example, if

f(x) = 2x-7
then solve for x to get f ^-1
y = 2x-7
(y+7)/2 = x
so, f ^-1(x) = (x+7)/2

Now,

f ^-1(f(x)) = (f(x)+7)/2
= ((2x-7)+7)/2
= (2x)/2
= x

and
f(f ^-1(x)) = 2f ^-1(x) - 7
= 2*(x+7)/2 - 7
= x+7-7
= x

Using values, just plug 'em in:

f(3) = 6-7 = -1
f ^-1(-1) = (-1+7)/2 = 3