Solve f^-1(x)=-x+8/5

$$f ^ { - 1 } ( x ) = \frac { - x + 8 } { 5 }$$

Solve for f

$$f=-\frac{5x}{x-8}$$

$$x\neq 0\text{ and }x\neq 8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5f^{-1}x=-x+8$$

Reorder the terms.

$$5\times \frac{1}{f}x=8-x$$

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

$$5\times 1x=f\times 8-xf$$

Multiply 5 and 1 to get 5.

$$5x=f\times 8-xf$$

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

$$f\times 8-xf=5x$$

Combine all terms containing f.

$$\left(8-x\right)f=5x$$

Divide both sides by 8-x.

$$\frac{\left(8-x\right)f}{8-x}=\frac{5x}{8-x}$$

Dividing by 8-x undoes the multiplication by 8-x.

$$f=\frac{5x}{8-x}$$

Variable f cannot be equal to 0.

$$f=\frac{5x}{8-x}\text{, }f\neq 0$$

Solve for x

$$x=\frac{8f}{f+5}$$

$$f\neq -5\text{ and }f\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5f^{-1}x=-x+8$$

Add x to both sides.

$$5f^{-1}x+x=8$$

Reorder the terms.

$$x+5\times \frac{1}{f}x=8$$

Multiply both sides of the equation by f.

$$fx+5\times 1x=8f$$

Multiply 5 and 1 to get 5.

$$fx+5x=8f$$

Combine all terms containing x.

$$\left(f+5\right)x=8f$$

Divide both sides by 5+f.

$$\frac{\left(f+5\right)x}{f+5}=\frac{8f}{f+5}$$

Dividing by 5+f undoes the multiplication by 5+f.

$$x=\frac{8f}{f+5}$$