Solve {l}{text{wykresfunkcji}g(x)=f(-x)}{f(x)={cc}{2}&{text{dla}xinlangle-4;-2)}{-x}&{text{dla}xinlangle-2;6rangle}}{text{ewykresyfunkcji}g(x)=f(-x)}

$$\left. \begin{array} { l } { \text { wykres funkcji } g ( x ) = f ( - x ) } \\ { f ( x ) = \left\{ \begin{array} { c c } { 2 } & { \text { dla } x \in \langle - 4 ; - 2 ) } \\ { - x } & { \text { dla } x \in \langle - 2 ; 6 \rangle } \end{array} \right.} \\ { \text { e wykresy funkcji } g ( x ) = f ( - x ) } \end{array} \right.$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&g=-f\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract f\left(-x\right) from both sides.

$$gx-f\left(-x\right)=0$$

Multiply -1 and -1 to get 1.

$$gx+fx=0$$

Combine all terms containing x.

$$\left(g+f\right)x=0$$

The equation is in standard form.

$$\left(f+g\right)x=0$$

Divide 0 by g+f.

$$x=0$$

Solve for x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&g=-f\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract f\left(-x\right) from both sides.

$$gx-f\left(-x\right)=0$$

Multiply -1 and -1 to get 1.

$$gx+fx=0$$

Combine all terms containing x.

$$\left(g+f\right)x=0$$

The equation is in standard form.

$$\left(f+g\right)x=0$$

Divide 0 by g+f.

$$x=0$$