Question

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Which functions are invertible?

Select EACH correct answer.

Answer 1

Second and fourth graph represent invertible functions.

Explanation:

According to the theory of functions, a function is invertible if it's one-to-one and surjective.

In addition, there's a graphic test called "horizontal line test". This test is used to know if a function is one-to-one. It consist in drawing an horizontal line across the graph, if the line intercept the function at one point, then that function is one-to-one, if the line intercept the function at two points, then that function is not one-to-one. And, if the function is one-to-one, then it can be invertible.

So, in the given graph, if we draw a horizontal line on each function, the first and third function aren't one-to-one, so they aren't invertible.

Therefore, by the horizontal line test, the second and fourth functions are one-to-one and they are invertible.

Answer 2

If a function is invertible, use the horizontal line test.

If a horizontal line intersects the graph at more than one point then it is not invertible.

The top right and bottom right graphs pass the horizontal line test, so are invertible