How to Determine the Inverse of Functions

The inverse reverses the function.

In mathematics, every function has two components: the function itself and its inverse. The inverse function reverses all the actions performed by the function. The inverse of a function uses the output solution to arrive back at the original values. Mathematicians denote the function by "f" and the inverse of the function by "f^-1." By using the inverse function, an individual can cross-check the function.

Instructions

1. Define your function. Many times, you need to define your function from a word problem. Read the word problem carefully and understand what you are expected to do. Set the limits on the function. The limit is the range within which the solution is supposed to lie. The maximum and minimum values of the function are determined by the limits.

2. Transpose your "x" and "y" values in the function. For example, suppose your function is y = 4x - 1. When you transpose the values, the equation would look like x = 4y - 1. You are only interchanging the "x" and the "y" values.

3. Solve the function for the value of "y." In the example, x = 4y - 1, the value of y would be equal to x/4 + 1/4. Solve the function using the same limits set before. Note that just because you calculated the inverse function, the limits of the function would not change. The maximum and minimum values would still remain to be the same.

References

• Analyze Math: Inverse Function
• Purplemath: Finding the Inverse of a Function
• Regents Prep Exam Center: Definition of Inverse Function