Solve y=sqrt{f(x)}

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

Solve for f

$$\left\{\begin{matrix}f=\frac{y^{2}}{x}\text{, }&y\geq 0\text{ and }x\neq 0\\f\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{fx}=y$$

Square both sides of the equation.

$$xf=y^{2}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{y^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{y^{2}}{x}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y^{2}}{f}\text{, }&y\geq 0\text{ and }f\neq 0\\x\in \mathrm{R}\text{, }&y=0\text{ and }f=0\end{matrix}\right.$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{fx}=y$$

Square both sides of the equation.

$$fx=y^{2}$$

Divide both sides by f.

$$\frac{fx}{f}=\frac{y^{2}}{f}$$

Dividing by f undoes the multiplication by f.

$$x=\frac{y^{2}}{f}$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{y^{2}}{x}\text{, }&x\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\\f\in \mathrm{C}\text{, }&y=0\text{ and }x=0\end{matrix}\right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y^{2}}{f}\text{, }&f\neq 0\text{ and }\left(y=0\text{ or }arg(y)<\pi \right)\\x\in \mathrm{C}\text{, }&y=0\text{ and }f=0\end{matrix}\right.$$