Solve y=f(x)=sqrt{x+1}-2

$$y = f ( x ) = \sqrt { x + 1 } - 2$$

Solve for x

$$x=\left(y+1\right)\left(y+3\right)$$

$$y+2\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{x+1}-2=y$$

Add 2 to both sides.

$$\sqrt{x+1}=y+2$$

Square both sides of the equation.

$$x+1=\left(y+2\right)^{2}$$

Subtract 1 from both sides of the equation.

$$x+1-1=\left(y+2\right)^{2}-1$$

Subtracting 1 from itself leaves 0.

$$x=\left(y+2\right)^{2}-1$$

Subtract 1 from \left(y+2\right)^{2}.

$$x=\left(y+1\right)\left(y+3\right)$$

Solve for x (complex solution)

$$x=\left(y+1\right)\left(y+3\right)$$

$$y=-2\text{ or }arg(y+2)<\pi$$

Solve for y

$$y=\sqrt{x+1}-2$$

$$x\geq -1$$