Solve y=sqrt{-x+4}-1

$$y = \sqrt { - x + 4 } - 1$$

Solve for x

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

$$y+1\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{-x+4}-1=y$$

Add 1 to both sides.

$$\sqrt{-x+4}=y+1$$

Square both sides of the equation.

$$-x+4=\left(y+1\right)^{2}$$

Subtract 4 from both sides of the equation.

$$-x+4-4=\left(y+1\right)^{2}-4$$

Subtracting 4 from itself leaves 0.

$$-x=\left(y+1\right)^{2}-4$$

Subtract 4 from \left(y+1\right)^{2}.

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

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{\left(y-1\right)\left(y+3\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{\left(y-1\right)\left(y+3\right)}{-1}$$

Divide \left(-1+y\right)\left(3+y\right) by -1.

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

Solve for x (complex solution)

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

$$y=-1\text{ or }arg(y+1)<\pi$$

Solve for y (complex solution)

$$y=\sqrt{4-x}-1$$

Solve for y

$$y=\sqrt{4-x}-1$$

$$x\leq 4$$