Solve fOg=f(g(x)=

$$f O g = f ( g ( x ) =$$

Solve for O (complex solution)

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

Steps for Solving Linear Equation

The equation is in standard form.

$$fgO=fgx$$

Divide both sides by fg.

$$\frac{fgO}{fg}=\frac{fgx}{fg}$$

Dividing by fg undoes the multiplication by fg.

$$O=\frac{fgx}{fg}$$

Divide fgx by fg.

$$O=x$$

Solve for f (complex solution)

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

Steps for Solving Linear Equation

Subtract fgx from both sides.

$$fOg-fgx=0$$

Reorder the terms.

$$-fgx+Ofg=0$$

Combine all terms containing f.

$$\left(-gx+Og\right)f=0$$

The equation is in standard form.

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

Divide 0 by -gx+Og.

$$f=0$$

Solve for O

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

Steps for Solving Linear Equation

The equation is in standard form.

$$fgO=fgx$$

Divide both sides by fg.

$$\frac{fgO}{fg}=\frac{fgx}{fg}$$

Dividing by fg undoes the multiplication by fg.

$$O=\frac{fgx}{fg}$$

Divide fgx by fg.

$$O=x$$

Solve for f

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

Steps for Solving Linear Equation

Subtract fgx from both sides.

$$fOg-fgx=0$$

Reorder the terms.

$$-fgx+Ofg=0$$

Combine all terms containing f.

$$\left(-gx+Og\right)f=0$$

The equation is in standard form.

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

Divide 0 by -gx+Og.

$$f=0$$