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

1 Answer
Jun 19, 2018

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]}