Solve f^-1=3x+2/5

$$f ^ { - 1 } = \frac { 3 x + 2 } { 5 }$$

Solve for f

$$f=\frac{5}{3x+2}$$

$$x\neq -\frac{2}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5f^{-1}=3x+2$$

Reorder the terms.

$$5\times \frac{1}{f}=3x+2$$

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

$$5\times 1=3xf+f\times 2$$

Multiply 5 and 1 to get 5.

$$5=3xf+f\times 2$$

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

$$3xf+f\times 2=5$$

Combine all terms containing f.

$$\left(3x+2\right)f=5$$

Divide both sides by 3x+2.

$$\frac{\left(3x+2\right)f}{3x+2}=\frac{5}{3x+2}$$

Dividing by 3x+2 undoes the multiplication by 3x+2.

$$f=\frac{5}{3x+2}$$

Variable f cannot be equal to 0.

$$f=\frac{5}{3x+2}\text{, }f\neq 0$$

Solve for x

$$x=-\frac{2}{3}+\frac{5}{3f}$$

$$f\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5f^{-1}=3x+2$$

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

$$3x+2=5f^{-1}$$

Subtract 2 from both sides.

$$3x=5f^{-1}-2$$

Reorder the terms.

$$3x=-2+5\times \frac{1}{f}$$

Multiply both sides of the equation by f.

$$3xf=f\left(-2\right)+5\times 1$$

Multiply 5 and 1 to get 5.

$$3xf=f\left(-2\right)+5$$

The equation is in standard form.

$$3fx=5-2f$$

Divide both sides by 3f.

$$\frac{3fx}{3f}=\frac{5-2f}{3f}$$

Dividing by 3f undoes the multiplication by 3f.

$$x=\frac{5-2f}{3f}$$

Divide -2f+5 by 3f.

$$x=-\frac{2}{3}+\frac{5}{3f}$$