Find the Domain and Range 3+ square root of x-1

$3 + \sqrt{x - 1}$

Step 1

Set the radicand in $\sqrt{x - 1}$ greater than or equal to $0$ to find where the expression is defined.

$x - 1 \geq 0$

Step 2

Add $1$ to both sides of the inequality.

$x \geq 1$

Step 3

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

Interval Notation:

$[1, \infty)$

Set-Builder Notation:

${x | x \geq 1}$

Step 4

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

Interval Notation:

$[3, \infty)$

Set-Builder Notation:

${y | y \geq 3}$

Step 5

Determine the domain and range.

Domain: $[1, \infty), {x | x \geq 1}$

Range: $[3, \infty), {y | y \geq 3}$

Step 6