Solve f^-1(x)=21-6x/5

$$f ^ { - 1 } ( x ) = \frac { 21 - 6 x } { 5 }$$

Solve for f

$$f=-\frac{5x}{3\left(2x-7\right)}$$

$$x\neq 0\text{ and }x\neq \frac{7}{2}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5f^{-1}x=21-6x$$

Reorder the terms.

$$5\times \frac{1}{f}x=-6x+21$$

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

$$5\times 1x=-6xf+f\times 21$$

Multiply 5 and 1 to get 5.

$$5x=-6xf+f\times 21$$

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

$$-6xf+f\times 21=5x$$

Combine all terms containing f.

$$\left(-6x+21\right)f=5x$$

The equation is in standard form.

$$\left(21-6x\right)f=5x$$

Divide both sides by -6x+21.

$$\frac{\left(21-6x\right)f}{21-6x}=\frac{5x}{21-6x}$$

Dividing by -6x+21 undoes the multiplication by -6x+21.

$$f=\frac{5x}{21-6x}$$

Divide 5x by -6x+21.

$$f=\frac{5x}{3\left(7-2x\right)}$$

Variable f cannot be equal to 0.

$$f=\frac{5x}{3\left(7-2x\right)}\text{, }f\neq 0$$

Solve for x

$$x=\frac{21f}{6f+5}$$

$$f\neq -\frac{5}{6}\text{ and }f\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$5f^{-1}x=21-6x$$

Add 6x to both sides.

$$5f^{-1}x+6x=21$$

Reorder the terms.

$$6x+5\times \frac{1}{f}x=21$$

Multiply both sides of the equation by f.

$$6xf+5\times 1x=21f$$

Multiply 5 and 1 to get 5.

$$6xf+5x=21f$$

Combine all terms containing x.

$$\left(6f+5\right)x=21f$$

Divide both sides by 5+6f.

$$\frac{\left(6f+5\right)x}{6f+5}=\frac{21f}{6f+5}$$

Dividing by 5+6f undoes the multiplication by 5+6f.

$$x=\frac{21f}{6f+5}$$