Algebra Examples

f (x) = \sqrt{x - 3}

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

Step 1

Set the radicand in

\sqrt{x - 3}

$\sqrt{x - 3}$ greater than or equal to

0

$0$ to find where the expression is defined.

x - 3 \geq 0

$x - 3 \geq 0$

Step 2

Add

3

$3$ to both sides of the inequality.

x \geq 3

$x \geq 3$

Step 3

The domain is all values of

x

$x$ that make the expression defined.

Interval Notation:

[3, \infty)

$[3, \infty)$

Set-Builder Notation:

{x | x \geq 3}

${x | x \geq 3}$

Step 4

The range is the set of all valid

y

$y$ values. Use the graph to find the range.

Interval Notation:

[0, \infty)

$[0, \infty)$

Set-Builder Notation:

{y | y \geq 0}

${y | y \geq 0}$

Step 5

Determine the domain and range.

Domain:

[3, \infty), {x | x \geq 3}

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

Range:

[0, \infty), {y | y \geq 0}

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

Step 6

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$