inverse function

Question

find the inverse for each of the following functions f(x)=ln(2+4x)

Answer 1

Given function f(x) = ln(2+4x)

Replace the function notation f(x) by y.

y = ln(2+4x)

interchange the roles x and y

x = ln(2+4y)

Raise by e on each sides.

e^x = 2+4y

Subtract 2 from each side.

e^x-2 = 2-2+4y

e^x-2 = 4y

Divide to each side by 4.

(e^x-2)/4 = 4y/4

1/4(e^x-2) = y

Replace the variable y by the nverse notation f^-1(x).

So the f^-1(x) = 1/4(e^x-2).