Solve y=f^-1(x)

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

Solve for f

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

Steps for Solving Linear Equation

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

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

Reorder the terms.

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

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

$$1x=yf$$

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

$$yf=1x$$

Reorder the terms.

$$fy=x$$

The equation is in standard form.

$$yf=x$$

Divide both sides by y.

$$\frac{yf}{y}=\frac{x}{y}$$

Dividing by y undoes the multiplication by y.

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

Variable f cannot be equal to 0.

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

Solve for x

$$x=fy$$

$$f\neq 0$$

Solution Steps

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

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

Reorder the terms.

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

Multiply both sides of the equation by f.

$$1x=yf$$

Reorder the terms.

$$x=fy$$