Solve f^-1=3x-5/4

$$f ^ { - 1 } = \frac { 3 x - 5 } { 4 }$$

Solve for f

$$f=-\frac{4}{5-3x}$$

$$x\neq \frac{5}{3}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$4f^{-1}=3x-5$$

Reorder the terms.

$$4\times \frac{1}{f}=3x-5$$

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

$$4\times 1=3xf+f\left(-5\right)$$

Multiply 4 and 1 to get 4.

$$4=3xf+f\left(-5\right)$$

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

$$3xf+f\left(-5\right)=4$$

Combine all terms containing f.

$$\left(3x-5\right)f=4$$

Divide both sides by 3x-5.

$$\frac{\left(3x-5\right)f}{3x-5}=\frac{4}{3x-5}$$

Dividing by 3x-5 undoes the multiplication by 3x-5.

$$f=\frac{4}{3x-5}$$

Variable f cannot be equal to 0.

$$f=\frac{4}{3x-5}\text{, }f\neq 0$$

Solve for x

$$x=\frac{5}{3}+\frac{4}{3f}$$

$$f\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4.

$$4f^{-1}=3x-5$$

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

$$3x-5=4f^{-1}$$

Add 5 to both sides.

$$3x=4f^{-1}+5$$

Reorder the terms.

$$3x=5+4\times \frac{1}{f}$$

Multiply both sides of the equation by f.

$$3xf=f\times 5+4\times 1$$

Multiply 4 and 1 to get 4.

$$3xf=f\times 5+4$$

The equation is in standard form.

$$3fx=5f+4$$

Divide both sides by 3f.

$$\frac{3fx}{3f}=\frac{5f+4}{3f}$$

Dividing by 3f undoes the multiplication by 3f.

$$x=\frac{5f+4}{3f}$$

Divide 5f+4 by 3f.

$$x=\frac{5}{3}+\frac{4}{3f}$$