What is the inverse of the function f(x) = [(lnx)-5]/2

Given the function f(x) = [ln(x)] - 5
/2

We need to find the inverse function f^-1
(x).

Let y= [ln(x) -5)/2

We will need
to isolate x.

First we will multiply by
2.

==> 2y= ln x - 5

Now we will
add 5 to both sides.

==> 2y + 5 = ln
x

Now we will rewrite into exponent
form.

==> x= e^(2y+5)

Now we
will replace x and y.

==> y=
e^(2x+5)

Then the inverse function
is:

f^-1 (x) =
e^(2x+5)