Find the Domain and Range square root of x-2+1

$\sqrt{x - 2} + 1$

Step 1

Set the radicand in $\sqrt{x - 2}$ greater than or equal to $0$ to find where the expression is defined.

$x - 2 \geq 0$

Step 2

Add $2$ to both sides of the inequality.

$x \geq 2$

Step 3

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

Interval Notation:

$[2, \infty)$

Set-Builder Notation:

${x | x \geq 2}$

Step 4

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

Interval Notation:

$[1, \infty)$

Set-Builder Notation:

${y | y \geq 1}$

Step 5

Determine the domain and range.

Domain: $[2, \infty), {x | x \geq 2}$

Range: $[1, \infty), {y | y \geq 1}$

Step 6