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

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

Solve for f

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$fxx=1+x\left(-1\right)$$

Multiply x and x to get x^{2}.

$$fx^{2}=1+x\left(-1\right)$$

The equation is in standard form.

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

Divide both sides by x^{2}.

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

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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{4f+1}-1}{2f}\text{; }x=-\frac{\sqrt{4f+1}+1}{2f}\text{, }&f\neq 0\\x=1\text{, }&f=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{4f+1}-1}{2f}\text{; }x=-\frac{\sqrt{4f+1}+1}{2f}\text{, }&f\neq 0\text{ and }f\geq -\frac{1}{4}\\x=1\text{, }&f=0\end{matrix}\right.$$