Find the Roots (Zeros) f(x) = square root of 2x-1

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

Set $\sqrt{2 x} - 1$ equal to $0$ .

$\sqrt{2 x} - 1 = 0$

Solve for $x$ .

Add $1$ to both sides of the equation.

$\sqrt{2 x} = 1$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 x}}^{2} = 1^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x}$ as ${(2 x)}^{\frac{1}{2}}$ .

${({(2 x)}^{\frac{1}{2}})}^{2} = 1^{2}$

Simplify the left side.

Simplify ${({(2 x)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(2 x)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(2 x)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Rewrite the expression.

${(2 x)}^{1} = 1^{2}$

Simplify.

$2 x = 1^{2}$

Simplify the right side.

One to any power is one.

$2 x = 1$

Divide each term in $2 x = 1$ by $2$ and simplify.

Divide each term in $2 x = 1$ by $2$ .

$\frac{2 x}{2} = \frac{1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{1}{2}$

Divide $x$ by $1$ .

$x = \frac{1}{2}$