Question

How do you find the inverse of `y=x^2` and is it a function?

Answer 1

Inverse: `+-sqrtx`
Not a function - But see below.

Explanation:

`y=x^2`

Since `x^2 = y` then `x=+-sqrty`

Let `f^-1(x)` be the inverse of `y`

Thus, `f^-1(x) = +-sqrtx`

By definition, a function is a process or a relation that associates each element x in the domain of the function, to a single element y in the co-domain of the function.

In this case, a single element in the domain of `f(x)` associates with two elements in the co-domain. Hence, `f(x)` is not a function.

graph{y^2-x=0 [-10, 10, -5, 5]}

However, if we limit the co-domain to the primary (positive) values of `sqrtx`, then `f(x)` is a function.

graph{sqrtx [-10, 10, -5, 5]}