Problem

Let f(x) be a function which contains the points

Which of the following functions could be its inverse?

a.

b.

c.

Solution

Method 1

Since the function f takes in the value of x in the table and outputs the value of y, f ^–1 will take as inputs the values of y in the table and output the values of x. So, we can just calculate the values of each function for each y given in the table, and choose the function whose outputs match the column of x values.

Looking at the tables, we can conclude that only a could be the inverse of f.

Method 2

Another way to solve this problem is to take each of the candidates for the inverse and find its inverse, and see which one can give us a table of values x and y identical to the one at the beginning of this problem.

a.

b.

c.

Therefore, a is the inverse function to f.