EXPLORING INVERSE FUNCTIONS
Computing Inverse Functions

Computing Inverse Functions

Recall that the input and output values of inverse functions are interchanged. Thus, if we start with an original function y=f(x), then the relation x=f(y) will describe the inverse function. In fact, if we graph the relations y=f(x) and x=f(y), we will see that the two graphs are indeed reflections in the line y=x.

If follows that if we want to compute the formula for the inverse function, i.e., write it as a function of x, we just need to start with the relation x=f(y) and solve for y (if possible). Here are several examples:

Example 1:

• Start with the original function: y=2x+3
• Interchange x and y: x=2y+3
• Solve for y: y=(x-3)/2.

Example 2:

• Start with the original function: y=x³-1
• Interchange x and y: x=y³-1
• Solve for y: y=cubert(x+1), where "cubert" is the cube root function.

Example 3:

• Start with the original function: y=2^x+1
• Interchange x and y: x=2^y+1
• Solve for y: y=log₂x-1

On the next page you can practice computing inverse functions and seeing their graphs.

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