Question

find the domain of the function. f(x) = \frac{1}{\sqrt{x - 4}} the domain of f(x) is (type your answer in interval notation.)

Explanation:

Step1: Determine the non - negativity of the radicand

For the square root $\sqrt{x - 4}$ to be a real number, we need $x-4\geq0$. Also, since it is in the denominator, $x - 4
eq0$. So we solve the inequality $x-4>0$.
$x-4>0$

Step2: Solve the inequality

Add 4 to both sides of the inequality $x - 4>0$.
$x>4$

Answer:

$(4,+\infty)$