Solve y=f(x)=sqrt{3x-2}

$$y = f ( x ) = \sqrt { 3 x - 2 }$$

Solve for x

$$x=\frac{y^{2}+2}{3}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{3x-2}=y$$

Square both sides of the equation.

$$3x-2=y^{2}$$

Add 2 to both sides of the equation.

$$3x-2-\left(-2\right)=y^{2}-\left(-2\right)$$

Subtracting -2 from itself leaves 0.

$$3x=y^{2}-\left(-2\right)$$

Subtract -2 from y^{2}.

$$3x=y^{2}+2$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{y^{2}+2}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{y^{2}+2}{3}$$

Solve for x (complex solution)

$$x=\frac{y^{2}+2}{3}$$

$$arg(y)<\pi \text{ or }y=0$$

Solve for y

$$y=\sqrt{3x-2}$$

$$x\geq \frac{2}{3}$$