Solve f(x)=alpha/x

$$f ( x ) = \frac { \alpha } { x }$$

Solve for f

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$fxx=\alpha$$

Multiply x and x to get x^{2}.

$$fx^{2}=\alpha$$

The equation is in standard form.

$$x^{2}f=\alpha$$

Divide both sides by x^{2}.

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

Dividing by x^{2} undoes the multiplication by x^{2}.

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-f^{-\frac{1}{2}}\sqrt{\alpha }\text{; }x=f^{-\frac{1}{2}}\sqrt{\alpha }\text{, }&\alpha \neq 0\text{ and }f\neq 0\\x\neq 0\text{, }&\alpha =0\text{ and }f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{\alpha }{f}}\text{; }x=-\sqrt{\frac{\alpha }{f}}\text{, }&\left(f<0\text{ and }\alpha <0\right)\text{ or }\left(f>0\text{ and }\alpha >0\right)\\x\neq 0\text{, }&\alpha =0\text{ and }f=0\end{matrix}\right.$$