Solve y=f(x)=1/x-2

$$y = f ( x ) = \frac { 1 } { x - 2 }$$

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 2 since division by zero is not defined. Multiply both sides of the equation by x-2.

$$y\left(x-2\right)=1$$

Use the distributive property to multiply y by x-2.

$$yx-2y=1$$

Add 2y to both sides.

$$yx=1+2y$$

The equation is in standard form.

$$yx=2y+1$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{2y+1}{y}$$

Dividing by y undoes the multiplication by y.

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

Divide 1+2y by y.

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

Variable x cannot be equal to 2.

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

Solve for y

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

$$x\neq 2$$