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?

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.