Solve f^-1(x)=x*20/3

$$f ^ { - 1 } ( x ) = x \times \frac { 20 } { 3 }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=0\text{, }&f\neq 0\\x\in \mathrm{C}\text{, }&f=\frac{3}{20}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x\times \frac{20}{3} from both sides.

$$f^{-1}x-x\times \frac{20}{3}=0$$

Reorder the terms.

$$\frac{1}{f}x-\frac{20}{3}x=0$$

Multiply both sides of the equation by 3f, the least common multiple of f,3.

$$3\times 1x-\frac{20}{3}x\times 3f=0$$

Multiply 3 and 1 to get 3.

$$3x-\frac{20}{3}x\times 3f=0$$

Multiply -\frac{20}{3} and 3 to get -20.

$$3x-20xf=0$$

Combine all terms containing x.

$$\left(3-20f\right)x=0$$

Divide 0 by 3-20f.

$$x=0$$

Solve for f

$$\left\{\begin{matrix}\\f=\frac{3}{20}=0.15\text{, }&\text{unconditionally}\\f\neq 0\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$\frac{1}{f}x=\frac{20}{3}x$$

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3f, the least common multiple of f,3.

$$3\times 1x=\frac{20}{3}x\times 3f$$

Multiply 3 and 1 to get 3.

$$3x=\frac{20}{3}x\times 3f$$

Multiply \frac{20}{3} and 3 to get 20.

$$3x=20xf$$

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

$$20xf=3x$$

Divide both sides by 20x.

$$\frac{20xf}{20x}=\frac{3x}{20x}$$

Dividing by 20x undoes the multiplication by 20x.

$$f=\frac{3x}{20x}$$

Divide 3x by 20x.

$$f=\frac{3}{20}$$

Solve for x

$$\left\{\begin{matrix}x=0\text{, }&f\neq 0\\x\in \mathrm{R}\text{, }&f=\frac{3}{20}\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x\times \frac{20}{3} from both sides.

$$f^{-1}x-x\times \frac{20}{3}=0$$

Reorder the terms.

$$\frac{1}{f}x-\frac{20}{3}x=0$$

Multiply both sides of the equation by 3f, the least common multiple of f,3.

$$3\times 1x-\frac{20}{3}x\times 3f=0$$

Multiply 3 and 1 to get 3.

$$3x-\frac{20}{3}x\times 3f=0$$

Multiply -\frac{20}{3} and 3 to get -20.

$$3x-20xf=0$$

Combine all terms containing x.

$$\left(3-20f\right)x=0$$

Divide 0 by 3-20f.

$$x=0$$