Question

What function is the square root parent function, F(x) = e="\sqrt{x}" alt="\sqrt{x}" align="absmiddle" class="latex-formula"> the inverse of?
A. $F(x) = x^2$, where $x$ ≥ $0$
B. $F(x) = |x|$
C. $F(x)=\frac{1}{\sqrt{x} }$
D. $F(x) = x^2$

Answer 1

You can think of an inverse function as a function that “unwraps” x from whatever operations are attached to it. In the case of F(x) = √x, we can ”unwrap” x by squaring it. This narrows our options down to either A or D. Keep in mind that since there are no real number solutions to the square root of a negative number, we need to limit our domain to non-negative values. In other words, x ≥ 0. With that restriction, our answer is A.

Answer 2

Hello!

The answer is:

The inverse of the given function is:

A. $f(x)^{-1}=x^{2}$

Where,

$x\geq 0$

Why?

Inversing a function involves inversing the function variables. If we want to inverse a function, we need to rewrite the variable "x" with "y" and rewrite the variable "y" with "x", and then, isolate the variable "y".

Also, the domain of the original function will be the range of its inverse function, and the range of the original function, will be the domain of the its inverse function.

We are given the function:

$f(x)=\sqrt{x}$

$f(x)=y=\sqrt{x}$

So, inversing we have:

$y=\sqrt{x}$

$x=\sqrt{y}$

$(x)^{2}=(\sqrt{y})^{2}\\\\x^{2}=(y^{\frac{1}{2}})^{2}\\\\x^{2}=y^{\frac{2}{2} }\\\\x^{2}=y$

So, we have that the given function is only "part" of its inverse function, since negative square roots does not exist, it means that the domain of the given function starts from the number 0 taking only positive numbers.

Hence, we have that the answer is:

A. $F(x)=x^{2}$

Where,

$x\geq 0$

Have a nice day!