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
    1. f(f -1(x)) = f(x) = ln(ex + 3 - 2 + 2) - 3

        = ln(ex + 3) - 3


        = (x + 3) - 3

        =x

    2. 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.






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