Question

How do you find the inverse of `y=3x^2-5`?

Answer 1

It depends on which inverse you want.

Explanation:

The additive inverse is what we need to add in order to get `0`.
In this case `-3x^2+5`

The multiplicative inverse is what we need to multiply be to get `1`.
In this case `1/(3x^2-5)`

The inverse function is the function that "undoes" what this function does. (It is what we need to compose with to get the identity function.)
In this case, there is no inverse function.
`y = 3x^2 -5` is not one-to-one.
We get the same `y` values for `x` values `1` and `-1` (or any other `a` and `-a`.)