Question

Find the domain of the function.

$f\left(x\right)=\frac{3}{\sqrt{x-4}}$

Short answer

The domain of the given function is $\left(4,\infty \right)$.

Step-by-step solution

Step 1. Definition of domain.

The set of all input values of a function is known as the domain of the function.

Step 2. Given information.

The given function is:

$f\left(x\right)=\frac{3}{\sqrt{x-4}}$

Step 3. Domain of the given function.

The given function is a rational function. The numerator is a constant and it is defined for all real values of x.

Denominator is defined if the radicand is non negative, i.e.,$x-4\ge 0$but the denominator cannot be equal to $0$, therefore the function is defined if:

localid="1644603268864" $\begin{array}{c}x-4>0\\ x>4\end{array}$

The given function is defined for all real values of$x$that are greater than $4$.

Thus, the domain of the given function is $\left(4,\infty \right)$.