Solve f^-1(x)=x^2

$$f ^ { - 1 } ( x ) = x ^ { 2 }$$

Solve for f

$$\left\{\begin{matrix}f=\frac{1}{x}\text{, }&x\neq 0\\f\neq 0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

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

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

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

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

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

Reorder the terms.

$$fx^{2}=x$$

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Divide x by x^{2}.

$$f=\frac{1}{x}$$

Variable f cannot be equal to 0.

$$f=\frac{1}{x}\text{, }f\neq 0$$

Solve for x

$$x=\frac{1}{f}$$

$$x=0\text{, }f\neq 0$$