Question

find the domain of the function.

$f(x)=\frac{5x}{sqrt{x - 9}}$

the domain is . (type your answer in interval notation.)

Explanation:

Step1: Determine the denominator condition

The denominator $\sqrt{x - 9}$ cannot be zero and the expression inside the square - root must be non - negative. For $\sqrt{x - 9}
eq0$, we have $x-9
eq0$, and for the square - root to be well - defined, $x - 9>0$.
$x-9>0$

Step2: Solve the inequality

Add 9 to both sides of the inequality $x - 9>0$.
$x>9$

Answer:

$(9,+\infty)$