Solve f(x+4)=(-2-x)=f(x)

$$f ( x + 4 ) = ( - 2 - x ) = f ( x )$$

Solve for f

$$f=-1-\frac{2}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$fx=-2-x$$

The equation is in standard form.

$$xf=-x-2$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{-x-2}{x}$$

Dividing by x undoes the multiplication by x.

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

Divide -2-x by x.

$$f=-1-\frac{2}{x}$$

Solve for x

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

$$f\neq -1$$

Steps for Solving Linear Equation

Subtract fx from both sides.

$$-2-x-fx=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-x-fx=2$$

Combine all terms containing x.

$$\left(-1-f\right)x=2$$

The equation is in standard form.

$$\left(-f-1\right)x=2$$

Divide both sides by -1-f.

$$\frac{\left(-f-1\right)x}{-f-1}=\frac{2}{-f-1}$$

Dividing by -1-f undoes the multiplication by -1-f.

$$x=\frac{2}{-f-1}$$

Divide 2 by -1-f.

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