Solve f_{2}:y=x^4-3

$$f _ { 2 } : y = x ^ { 4 } - 3$$

Solve for f_2

$$f_{2}=y\left(x^{4}-3\right)$$

$$y\neq 0$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{y}f_{2}=x^{4}-3$$

Divide both sides by y^{-1}.

$$\frac{\frac{1}{y}f_{2}y}{1}=\frac{\left(x^{4}-3\right)y}{1}$$

Dividing by y^{-1} undoes the multiplication by y^{-1}.

$$f_{2}=\frac{\left(x^{4}-3\right)y}{1}$$

Divide x^{4}-3 by y^{-1}.

$$f_{2}=y\left(x^{4}-3\right)$$

Solve for x (complex solution)

$$x=i\sqrt[4]{\frac{f_{2}}{y}+3}$$

$$x=\sqrt[4]{\frac{f_{2}}{y}+3}$$

$$x=-\sqrt[4]{\frac{f_{2}}{y}+3}$$

$$x=-i\sqrt[4]{\frac{f_{2}}{y}+3}\text{, }y\neq 0$$

Solve for x

$$x=\sqrt[4]{\frac{f_{2}}{y}+3}$$

$$x=-\sqrt[4]{\frac{f_{2}}{y}+3}\text{, }\left(f_{2}\leq -3y\text{ and }y<0\right)\text{ or }\left(f_{2}\geq -3y\text{ and }y>0\right)\text{ or }\left(y\neq 0\text{ and }f_{2}=-3y\right)$$