Solve f^-1(x)=pmsqrt{x+3}

$$f ^ { - 1 } ( x ) = \pm \sqrt { x + 3 }$$

Solve for f (complex solution)

$$\left\{\begin{matrix}f=\frac{x}{±\sqrt{x+3}}\text{, }&x\neq 0\text{ and }±\sqrt{x+3}\neq 0\\f\neq 0\text{, }&±\sqrt{3}=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$\frac{1}{f}x=±\sqrt{x+3}$$

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by f.

$$1x=f\left(±\sqrt{x+3}\right)$$

Swap sides so that all variable terms are on the left hand side.

$$f\left(±\sqrt{x+3}\right)=1x$$

Reorder the terms.

$$f\left(±\sqrt{x+3}\right)=x$$

The equation is in standard form.

$$\left(±\sqrt{x+3}\right)f=x$$

Divide both sides by ±\sqrt{x+3}.

$$\frac{\left(±\sqrt{x+3}\right)f}{±\sqrt{x+3}}=\frac{x}{±\sqrt{x+3}}$$

Dividing by ±\sqrt{x+3} undoes the multiplication by ±\sqrt{x+3}.

$$f=\frac{x}{±\sqrt{x+3}}$$

Variable f cannot be equal to 0.

$$f=\frac{x}{±\sqrt{x+3}}\text{, }f\neq 0$$

Solve for f

$$\left\{\begin{matrix}f=\frac{x}{±\sqrt{x+3}}\text{, }&x\neq 0\text{ and }±\sqrt{x+3}\neq 0\text{ and }x\geq -3\\f\neq 0\text{, }&x=0\text{ and }±\sqrt{3}=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$\frac{1}{f}x=±\sqrt{x+3}$$

Variable f cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by f.

$$1x=f\left(±\sqrt{x+3}\right)$$

Swap sides so that all variable terms are on the left hand side.

$$f\left(±\sqrt{x+3}\right)=1x$$

Reorder the terms.

$$f\left(±\sqrt{x+3}\right)=x$$

The equation is in standard form.

$$\left(±\sqrt{x+3}\right)f=x$$

Divide both sides by ±\sqrt{x+3}.

$$\frac{\left(±\sqrt{x+3}\right)f}{±\sqrt{x+3}}=\frac{x}{±\sqrt{x+3}}$$

Dividing by ±\sqrt{x+3} undoes the multiplication by ±\sqrt{x+3}.

$$f=\frac{x}{±\sqrt{x+3}}$$

Variable f cannot be equal to 0.

$$f=\frac{x}{±\sqrt{x+3}}\text{, }f\neq 0$$