Solve f(x)=x^2+1yg(x)=4x+3

$$f ( x ) = x ^ { 2 } + 1 y g ( x ) = 4 x + 3$$

Solve for g (complex solution)

$$\left\{\begin{matrix}g=-\frac{x^{2}-4x-3}{xy}\text{, }&x\neq 0\text{ and }y\neq 0\\g\in \mathrm{C}\text{, }&\left(x=2-\sqrt{7}\text{ or }x=\sqrt{7}+2\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$1ygx=4x+3-x^{2}$$

Reorder the terms.

$$gxy=-x^{2}+4x+3$$

The equation is in standard form.

$$xyg=3+4x-x^{2}$$

Divide both sides by yx.

$$\frac{xyg}{xy}=\frac{3+4x-x^{2}}{xy}$$

Dividing by yx undoes the multiplication by yx.

$$g=\frac{3+4x-x^{2}}{xy}$$

Solve for g

$$\left\{\begin{matrix}g=-\frac{x^{2}-4x-3}{xy}\text{, }&x\neq 0\text{ and }y\neq 0\\g\in \mathrm{R}\text{, }&\left(x=2-\sqrt{7}\text{ or }x=\sqrt{7}+2\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract x^{2} from both sides.

$$1ygx=4x+3-x^{2}$$

Reorder the terms.

$$gxy=-x^{2}+4x+3$$

The equation is in standard form.

$$xyg=3+4x-x^{2}$$

Divide both sides by yx.

$$\frac{xyg}{xy}=\frac{3+4x-x^{2}}{xy}$$

Dividing by yx undoes the multiplication by yx.

$$g=\frac{3+4x-x^{2}}{xy}$$

Solve for x

$$x=\frac{\sqrt{28+\left(gy\right)^{2}-8gy}}{2}-\frac{gy}{2}+2$$

$$x=-\frac{\sqrt{28+\left(gy\right)^{2}-8gy}}{2}-\frac{gy}{2}+2$$