Solve f(x)=x+1quadyquadg(x)=x^2+2x-3

$$f ( x ) = x + 1 \quad y \quad g ( x ) = x ^ { 2 } + 2 x - 3$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=\frac{x^{2}+x-3}{xy}\text{, }&x\neq 0\text{ and }y\neq 0\\g\in \mathrm{C}\text{, }&\left(x=\frac{-\sqrt{13}-1}{2}\text{ or }x=\frac{\sqrt{13}-1}{2}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$1ygx=x^{2}+2x-3-x$$

Combine 2x and -x to get x.

$$1ygx=x^{2}+x-3$$

Reorder the terms.

$$gxy=x^{2}+x-3$$

The equation is in standard form.

$$xyg=x^{2}+x-3$$

Divide both sides by yx.

$$\frac{xyg}{xy}=\frac{x^{2}+x-3}{xy}$$

Dividing by yx undoes the multiplication by yx.

$$g=\frac{x^{2}+x-3}{xy}$$

Solve for g

$$\left\{\begin{matrix}g=\frac{x^{2}+x-3}{xy}\text{, }&x\neq 0\text{ and }y\neq 0\\g\in \mathrm{R}\text{, }&\left(x=\frac{-\sqrt{13}-1}{2}\text{ or }x=\frac{\sqrt{13}-1}{2}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$1ygx=x^{2}+2x-3-x$$

Combine 2x and -x to get x.

$$1ygx=x^{2}+x-3$$

Reorder the terms.

$$gxy=x^{2}+x-3$$

The equation is in standard form.

$$xyg=x^{2}+x-3$$

Divide both sides by yx.

$$\frac{xyg}{xy}=\frac{x^{2}+x-3}{xy}$$

Dividing by yx undoes the multiplication by yx.

$$g=\frac{x^{2}+x-3}{xy}$$

Solve for x

$$x=\frac{-\sqrt{13+\left(gy\right)^{2}-2gy}+gy-1}{2}$$

$$x=\frac{\sqrt{13+\left(gy\right)^{2}-2gy}+gy-1}{2}$$