# Find Inverse Function (2) - Tutorial

More tutorials on how to fin the inverse function analytically are presented. Detailed explanations to every step are also included.

 Example 1: Find the inverse function of f given by f(x) = ln(x + 2) - 3 Solution to example 1: Write the function as an equation. y = ln(x + 2) - 3 Rewrite the equation so that it is easily solved for x. ln(x + 2) = y + 3 Rewrite the above in exponential form. x + 2 = ey + 3 Solve for x. x = ey + 3 - 2 now write f-1(y) as follows . f -1(y) = ey + 3 - 2 or change x into y and y into x in the above to have f -1(x) = ex + 3 - 2 Check f(f -1(x)) = f(x) = ln(ex + 3 - 2 + 2) - 3 = ln(ex + 3) - 3 = (x + 3) - 3 =x f -1(f(x))=f -1(2x + 3) = e(ln(x + 2) - 3) + 3 - 2 = eln(x + 2) - 2 = x + 2 - 2 = x conclusion: The inverse of function f given above is f -1(x) = ex + 3 - 2 Matched Exercise 1: Find the inverse function of f given by f(x) = 2ln(x + 4) - 4 More links and references related to the inverse functions. Find the Inverse Functions - Calculator Find the Inverse Function - Questions Find the Inverse Function (1) - Tutorial. Definition of the Inverse Function - Interactive Tutorial Find Inverse Of Cube Root Functions. Find Inverse Of Square Root Functions. Find Inverse Of Logarithmic Functions. Find Inverse Of Exponential Functions.