Answer
$f(x)$ is decreasing for all real numbers in the domain of $f(x)$. Also, the domain of $f(x)$ is $R-\{4\}$ (all real numbers except $4$).
Work Step by Step
To find the intervals in which $f(x)$ is increasing, or, decreasing we can use first derivative of $f(x)$.
Here, $f(x)=\dfrac{1}{x-4}$, so, $f'(x)=\dfrac{-1}{(x-4)^2}$.
Since, $(x-4)^2>0$, thus, $f'(x)<0$ for all $x$ in the domain.
Therefore, the function, $f(x)$ is decreasing for all $x$ in the domain by the first derivative test.
