Practice!

Sample Problem

Consider a function with the following table of values:

x

-3

-2

-1

0

1

2

3

f(x)

6

-4

1.5

3

1

4

-4

Does this function have an inverse function?

Solution

A function has an inverse function if and only if the function is one-to-one.

So another way to think about this question is according to the table of values for this function,

is f one-to-one? After close observation, see that both x-values x=-2 and x=3 have the same y value:

y=-4; therefore this function is NOT one-to-one and does NOT have an inverse function.

Note: the function could very well have an inverse, but its inverse will NOT pass the vertical line test i.e. its inverse is not a FUNCTION.