what's the inverse of f(x)=rootx?

Question

my teacher said the inverse can't be x^2 so i'm stuck...

Answer 1

The inverse of y=\sqrt{x} is y=x^2, x \geq 0. In other words, the inverse of the square root function is only the portion of y=x^2 where x is greater than or equal to zero.

We have restricted the domain because on its entire domain, y=x^2 is not one-to-one (it doesn't pass the horizontal line test) so it doesn't have an inverse on its entire domain.

Similarly, the inverse of y=x^2 for x less than or equal to 0 is y=-\sqrt{x}.

Answer 2

Let's restrict our discussion to real numbers.

There are two issues with "finding a square root".

One is that you can't do it for negative numbers, and the other is that you can get two answers. The first issue says that your domain needs to be within nonnegative numbers, and the second says you probably want to restrict the range to be nonnegative numbers as well. This idea of domains and ranges and having the power to control them is pretty sophisticated and confusing to students. If your teacher hasn't found a way to discuss these in class, it's not reasonable for you to answer the question in a meaningful way. No matter what, the inverse function will be x^2, but there will probably be some quibbling about the domain. But there won't be a better answer than "x^2 with domain the nonnegative answers".

With complex numbers it gets even more complicated.

Answer 3

the inverse of the square root of x is 1/rootx which is equivilent to x^-2

Answer 4

Hi:

The answer is Power x because any root inverse is power

for example

Square root (x) inverse is x squared)
Cube root (x) inverse is x cube
Fourth root of x inverse is x ^ 4

for the the general equation = root x inverse is the power x

Answer 5

x^2

Answer 6

it's (1/x)^2.

Answer 7

inverse number of f(x)=- rootx
but inverse function of f(x) x^2

Answer 8

yes

Answer 9

It is f^-1(x) = square(+ or -x).

Answer 10

rootx=f(x)