Solve f(x)=2xquadg(x)=x^2+1

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

Solve for g

$$g=\frac{1}{2}+\frac{1}{2x^{2}}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply x and x to get x^{2}.

$$2x^{2}g=x^{2}+1$$

Divide both sides by 2x^{2}.

$$\frac{2x^{2}g}{2x^{2}}=\frac{x^{2}+1}{2x^{2}}$$

Dividing by 2x^{2} undoes the multiplication by 2x^{2}.

$$g=\frac{x^{2}+1}{2x^{2}}$$

Divide x^{2}+1 by 2x^{2}.

$$g=\frac{1}{2}+\frac{1}{2x^{2}}$$

Solve for x (complex solution)

$$x=-\left(2g-1\right)^{-\frac{1}{2}}$$

$$x=\left(2g-1\right)^{-\frac{1}{2}}\text{, }g\neq \frac{1}{2}$$

Solve for x

$$x=\frac{1}{\sqrt{2g-1}}$$

$$x=-\frac{1}{\sqrt{2g-1}}\text{, }g>\frac{1}{2}$$