Solve g(x)=1/6f(x):f(x)=4x+12

$$g ( x ) = \frac { 1 } { 6 } f ( x ) : f ( x ) = 4 x + 12$$

Solve for f (complex solution)

$$f\neq 0$$

$$x=12-6\sqrt{6}\text{ or }x=6\sqrt{6}+12$$

Steps for Solving Linear Equation

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

$$\frac{1}{6}fxx=4xf+f\times 12$$

Multiply x and x to get x^{2}.

$$\frac{1}{6}fx^{2}=4xf+f\times 12$$

Subtract 4xf from both sides.

$$\frac{1}{6}fx^{2}-4xf=f\times 12$$

Subtract f\times 12 from both sides.

$$\frac{1}{6}fx^{2}-4xf-f\times 12=0$$

Multiply -1 and 12 to get -12.

$$\frac{1}{6}fx^{2}-4xf-12f=0$$

Combine all terms containing f.

$$\left(\frac{1}{6}x^{2}-4x-12\right)f=0$$

The equation is in standard form.

$$\left(\frac{x^{2}}{6}-4x-12\right)f=0$$

Divide 0 by \frac{1}{6}x^{2}-4x-12.

$$f=0$$

Variable f cannot be equal to 0.

$$f\in \emptyset$$

Solve for f

$$f\neq 0$$

$$x=6\sqrt{6}+12\text{ or }x=12-6\sqrt{6}$$

Steps for Solving Linear Equation

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

$$\frac{1}{6}fxx=4xf+f\times 12$$

Multiply x and x to get x^{2}.

$$\frac{1}{6}fx^{2}=4xf+f\times 12$$

Subtract 4xf from both sides.

$$\frac{1}{6}fx^{2}-4xf=f\times 12$$

Subtract f\times 12 from both sides.

$$\frac{1}{6}fx^{2}-4xf-f\times 12=0$$

Multiply -1 and 12 to get -12.

$$\frac{1}{6}fx^{2}-4xf-12f=0$$

Combine all terms containing f.

$$\left(\frac{1}{6}x^{2}-4x-12\right)f=0$$

The equation is in standard form.

$$\left(\frac{x^{2}}{6}-4x-12\right)f=0$$

Divide 0 by \frac{1}{6}x^{2}-12-4x.

$$f=0$$

Variable f cannot be equal to 0.

$$f\in \emptyset$$

Solve for x

$$x=6\sqrt{6}+12$$

$$x=12-6\sqrt{6}\text{, }f\neq 0$$