Question

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

Answer 1

`y = {x}^(2)`

Step-by-step 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 \: √(x)`

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