Solve y^-1=x^2

$$y ^ { - 1 } = x ^ { 2 }$$

Solve for y

$$y=\frac{1}{x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Reorder the terms.

$$\frac{1}{y}=x^{2}$$

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by y.

$$1=yx^{2}$$

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

$$yx^{2}=1$$

The equation is in standard form.

$$x^{2}y=1$$

Divide both sides by x^{2}.

$$\frac{x^{2}y}{x^{2}}=\frac{1}{x^{2}}$$

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

$$y=\frac{1}{x^{2}}$$

Variable y cannot be equal to 0.

$$y=\frac{1}{x^{2}}\text{, }y\neq 0$$

Solve for x (complex solution)

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

$$x=y^{-\frac{1}{2}}\text{, }y\neq 0$$

Solve for x

$$x=\frac{1}{\sqrt{y}}$$

$$x=-\frac{1}{\sqrt{y}}\text{, }y>0$$