Find the Domain and Range f(x) = square root of x-7+9

$f (x) = \sqrt{x - 7 + 9}$

Step 1

Set the radicand in $\sqrt{x - 7 + 9}$ greater than or equal to $0$ to find where the expression is defined.

$x - 7 + 9 \geq 0$

Step 2

Solve for $x$ .

Add $- 7$ and $9$ .

$x + 2 \geq 0$

Subtract $2$ from 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:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Step 5

Determine the domain and range.

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

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

Step 6