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

1 Answer
Alan N.
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]}

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