Question

Which functions are invertible?

Answer 1

The second and third functions are invertible. The first and fourth are not.

Explanation:

To tell whether a function is invertible, you can use the horizontal line test: Does any horizontal line intersect the graph of the function in at most one point?

If so then the function is invertible. If not, then it is not.

In the given examples, the functions depicted in the top left and bottom right corners fail the horizontal line test, but the ones in the top right and bottom left corner pass it.

Note that the graph of the inverse relation of a function is formed by reflecting the graph in the diagonal line `y=x`, thereby swapping `x` and `y`. This inverse relation is a function if and only if it passes the vertical line test.