Solve y=h^-1(x)

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

Solve for h

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

Steps for Solving Linear Equation

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

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

Reorder the terms.

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

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

$$1x=yh$$

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

$$yh=1x$$

Reorder the terms.

$$hy=x$$

The equation is in standard form.

$$yh=x$$

Divide both sides by y.

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

Dividing by y undoes the multiplication by y.

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

Variable h cannot be equal to 0.

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

Solve for x

$$x=hy$$

$$h\neq 0$$

Solution Steps

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

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

Reorder the terms.

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

Multiply both sides of the equation by h.

$$1x=yh$$

Reorder the terms.

$$x=hy$$