Find the Domain and Range f(x)=(x-3)^(1/2)

$f (x) = {(x - 3)}^{\frac{1}{2}}$

Convert expressions with fractional exponents to radicals.

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt{{(x - 3)}^{1}}$

Anything raised to $1$ is the base itself.

$\sqrt{x - 3}$

Set the radicand in $\sqrt{x - 3}$ greater than or equal to $0$ to find where the expression is defined.

$x - 3 \geq 0$

Add $3$ to both sides of the inequality.

$x \geq 3$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[3, \infty)$

Set-Builder Notation:

${x | x \geq 3}$

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Determine the domain and range.

Domain: $[3, \infty), {x | x \geq 3}$

Range: $[0, \infty), {y | y \geq 0}$