If f(x) = (3/2) x – 9/2, find f-1(x)

To determine the inverse function, we'll have to prove
that f(x) is bijective. We'll re-write f(x) factorizing  by
(3/2)

f(x) = (3/2)(x -
3)

Since x - 3 is a linear function, that is bijective,
then f(x) is bijective too.

We'll put f(x) =
y

y =  (3/2)(x - 3)

We'll
change y by x:

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

We'll have to determine
y:

We'll divide by 3/2:

2x/3 =
y - 3

We'll isolate y to the right side and then we'll use
symmetric property. We'll add 3 both sides:

y = 2x/3 +
3

The inverse function
is:

f^-1(x) =  2x/3 +
3