ANSWER
[tex]y = {x}^{2} [/tex]
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,
[tex]y = x[/tex]
and
[tex]y = 2x + 1[/tex]
will pass the horizontal line test.
But
[tex]y = {x}^{2} [/tex]
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:
[tex]y = {x}^{2} [/tex]
Interchange x and y.
[tex]x = {y}^{2} [/tex]
Solve for y,
[tex]y = \pm \: \sqrt{x} [/tex]
This is not a function, because it doesn't pass the vertical line test.
