Find the Domain f(x)=3/(x+2)- square root of x-3

$f (x) = \frac{3}{x + 2} - \sqrt{x - 3}$

Step 1

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

$x - 3 \geq 0$

Step 2

Add $3$ to both sides of the inequality.

$x \geq 3$

Step 3

Set the denominator in $\frac{3}{x + 2}$ equal to $0$ to find where the expression is undefined.

$x + 2 = 0$

Step 4

Subtract $2$ from both sides of the equation.

$x = - 2$

Step 5

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

Interval Notation:

$[3, \infty)$

Set-Builder Notation:

${x | x \geq 3}$

Step 6