When we have the square function defined by :
$y = x²$
This implies $x = \sqrt{y}$ or $x = - \sqrt{y}$, because the function $f(x) = \sqrt{x}$ can have only one image, and does return only a positive value.
We must plot its reciprocal function expressed in the original form :
$x = y²$
By doing so we preserve the negative part of the $y$ axis.
But considering that $f(x) = \sqrt{x}$ is the reciprocal function of $f(x) = x²$, we lost this negative part of the $y$ axis.
Then a question comes :
Is there any manner to cancel a square of a number, preserving its original value ?
Because taken a random number $a$ in $\mathbb{R}$, we would be tempted to say that if they are both reciprocals :
$(x^2)^{\frac{1}{2}} = x$
But it's not the case, because if $f(x) = \sqrt{x}$ returns only its positive result, then it implies that
$(x^2)^{\frac{1}{2}} = |x|$
A form of the equation which does not preserve the initial value of $x$, if $x < 0$.