Solve f^-1(x)=x-5/3

$$f ^ { - 1 } ( x ) = \frac { x - 5 } { 3 }$$

Solve for f

$$f=-\frac{3x}{5-x}$$

$$x\neq 0\text{ and }x\neq 5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3f^{-1}x=x-5$$

Reorder the terms.

$$3\times \frac{1}{f}x=x-5$$

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

$$3\times 1x=fx+f\left(-5\right)$$

Multiply 3 and 1 to get 3.

$$3x=fx+f\left(-5\right)$$

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

$$fx+f\left(-5\right)=3x$$

Combine all terms containing f.

$$\left(x-5\right)f=3x$$

Divide both sides by x-5.

$$\frac{\left(x-5\right)f}{x-5}=\frac{3x}{x-5}$$

Dividing by x-5 undoes the multiplication by x-5.

$$f=\frac{3x}{x-5}$$

Variable f cannot be equal to 0.

$$f=\frac{3x}{x-5}\text{, }f\neq 0$$

Solve for x

$$x=-\frac{5f}{3-f}$$

$$f\neq 3\text{ and }f\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$3f^{-1}x=x-5$$

Subtract x from both sides.

$$3f^{-1}x-x=-5$$

Reorder the terms.

$$-x+3\times \frac{1}{f}x=-5$$

Multiply both sides of the equation by f.

$$-xf+3\times 1x=-5f$$

Multiply 3 and 1 to get 3.

$$-xf+3x=-5f$$

Combine all terms containing x.

$$\left(-f+3\right)x=-5f$$

The equation is in standard form.

$$\left(3-f\right)x=-5f$$

Divide both sides by 3-f.

$$\frac{\left(3-f\right)x}{3-f}=-\frac{5f}{3-f}$$

Dividing by 3-f undoes the multiplication by 3-f.

$$x=-\frac{5f}{3-f}$$