Question

Which of the following functions has an inverse that is not a function? y = x y = 2x + 1 y = x²

Answer 1

ANSWER

$y = {x}^{2}$

EXPLANATION

For a function to be an invertible, it must be a one-to-one function.

In other words , it's graph should pass the horizontal line test.

It is obvious that,

$y = x$

and

$y = 2x + 1$

will pass the horizontal line test.

But

$y = {x}^{2}$

has a v-shape and hence cannot pass the horizontal line test.

This means that y=x² is not invertible. That is, its inverse is not a function.

Let us quickly check that:

$y = {x}^{2}$

Interchange x and y.

$x = {y}^{2}$

Solve for y,

$y = \pm \: \sqrt{x}$

This is not a function, because it doesn't pass the vertical line test.