Question

Find the inverse of the function F(x) = 5+ln(x+1)

Answer 1

The inverse of a function is the function that undoes its operation. The notation for the inverse of the function f is f-1. In function notation this can be written like this.

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

Answer 2

y = 5/(x + 1)

Finding the inverse of ANY function f(x) requires these steps:
1) Change f(x) into y (if it's not changed already).
2) Interchange the x and y variables.
3) Solve for y. The result of y will be your function.
4) Change the y to f inverse of x, or f^(-1)(x).

Let's assume you started off with

f(x) = 5/(x + 1)

Change f(x) into y.

y = 5/(x + 1)

Interchange x and y.

x = 5/(y + 1)

Solve for y.

x(y + 1) = 5
y + 1 = 5/x
y = (5/x) - 1

Change y into f^(-1)(x) (concluding statement)

f^(-1)(x) = (5/x) - 1

This is the inverse of f(x) = 5/(x + 1)