Solve g(x)=x^3yF(x)=mx^3+b

$$g ( x ) = x ^ { 3 } y F ( x ) = m x ^ { 3 } + b$$

Solve for F (complex solution)

$$\left\{\begin{matrix}F=\frac{mx^{3}+b}{yx^{4}}\text{, }&x\neq 0\text{ and }y\neq 0\\F\in \mathrm{C}\text{, }&\left(b=0\text{ and }x=0\right)\text{ or }\left(b=-mx^{3}\text{ and }y=0\text{ and }x\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{4}yF=mx^{3}+b$$

The equation is in standard form.

$$yx^{4}F=mx^{3}+b$$

Divide both sides by x^{4}y.

$$\frac{yx^{4}F}{yx^{4}}=\frac{mx^{3}+b}{yx^{4}}$$

Dividing by x^{4}y undoes the multiplication by x^{4}y.

$$F=\frac{mx^{3}+b}{yx^{4}}$$

Solve for F

$$\left\{\begin{matrix}F=\frac{mx^{3}+b}{yx^{4}}\text{, }&x\neq 0\text{ and }y\neq 0\\F\in \mathrm{R}\text{, }&\left(b=0\text{ and }x=0\right)\text{ or }\left(b=-mx^{3}\text{ and }y=0\text{ and }x\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{4}yF=mx^{3}+b$$

The equation is in standard form.

$$yx^{4}F=mx^{3}+b$$

Divide both sides by x^{4}y.

$$\frac{yx^{4}F}{yx^{4}}=\frac{mx^{3}+b}{yx^{4}}$$

Dividing by x^{4}y undoes the multiplication by x^{4}y.

$$F=\frac{mx^{3}+b}{yx^{4}}$$

Solve for b

$$b=x^{3}\left(Fxy-m\right)$$