Solve f(x)=operatorname{sqrt}(x^2-3)

$$f ( x ) = \operatorname { sqrt } ( x ^ { 2 } - 3 )$$

Solve for f (complex solution)

$$f=\frac{\sqrt{x^{2}-3}}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=\sqrt{x^{2}-3}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{\sqrt{x^{2}-3}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{\sqrt{x^{2}-3}}{x}$$

Solve for f

$$f=\frac{\sqrt{x^{2}-3}}{x}$$

$$|x|\geq \sqrt{3}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=\sqrt{x^{2}-3}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{\sqrt{x^{2}-3}}{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{\sqrt{x^{2}-3}}{x}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\sqrt{3}\left(1-f^{2}\right)^{-\frac{1}{2}}\text{, }&f\neq 1\text{ and }f\neq -1\text{ and }\left(f=0\text{ or }arg(\left(3-3f^{2}\right)^{-\frac{1}{2}}f)<\pi \right)\\x=-\sqrt{3}\left(1-f^{2}\right)^{-\frac{1}{2}}\text{, }&f\neq 1\text{ and }f\neq -1\text{ and }\left(f=0\text{ or }arg(\left(1-f^{2}\right)^{-\frac{1}{2}}f)\geq \pi \right)\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=-\sqrt{\frac{3}{1-f^{2}}}\text{, }&f>-1\text{ and }f\leq 0\\x=\sqrt{\frac{3}{1-f^{2}}}\text{, }&f\geq 0\text{ and }f<1\end{matrix}\right.$$