Find the inverse of y = x/4 + 3. What can be said about fof^-1(x) of any function.

To determine the inverse, we'll have to write a expression
of a function, with respect to y, starting from original
function.

We'll write the given
function:

y = x/4 + 3

We'll
multiply by 4 both sides:

4y = x +
12

We'll use the symmetric
property:

x + 12 = 4y

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

x = 4y -
12

The inverse function
is:

f^-1(x) = 4x -
12

Now, we'll compose the
functions:

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

We'll substitute x by the f^-1(x) in the
expression of f(x):

f(f^-1(x)) = f^-1(x)/4 +
3

We'll substitute f^-1(x) by it's
expression:

f(f^-1(x)) = (4x - 12)/4 +
3

f(f^-1(x)) = 4x/4 - 12/4 +
3

f(f^-1(x)) = x - 3 + 3

We'll
eliminate like terms and we'll
get:

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