Describe how to find the inverse of function y=3x+12?

The inverse of the function f(x) is
f^-1(x).

To prove that f(x) has inverse, we'll have to
prove first that f(x) is bijective.

To prove that f(x) is
bijective, we'll have to prove that is one-to-one and on-to
function.

1) One-to-one
function.

We'll suppose that f(x1) =
f(x2)

We'll substitute f(x1) and f(x2) by their
expressions:

3x1 + 12= 3x2 +
12

We'll eliminate like
terms:

3x1 = 3x2

We'll divide
by 3:

x1 = x2

A function is
one-to-one if and only if for x1 = x2 => f(x1) =
f(x2).

2) On-to function:

For
a real y, we'll have to prove that it exists a real x.

y =
3x + 12

We'll isolate x to the right side. For this reason,
we'll subtract 12 both sides:

y - 12 =
3x

We'll use the symmetric
property:

3x = y - 12

We'll
divide by 3:

x = y/3 - 4

x is
a real number => f(x) is an on-to function

Since the
function is both, one to one and on-to function, then f(x) is
bijective.

If f(x) is bijective => f(x) is
invertible.

The requested inverse function of
f(x) = 3x + 12 is: f^-1(x) = x/3 - 4.