What is the domain of the function \(f(x)=\log_5(4-x)\)?

Correct answer: \(( -\infty,4)\)

For a logarithmic function, its argument must be positive. Thus, \(4-x>0\), which gives \(x<4\). Therefore, the domain is \(( -\infty,4)\). Option C wrongly includes \(4\); at \(x=4\), the argument is \(0\), and \(\log 0\) is undefined. Exam tip: In logarithmic domain questions, first set the expression inside the log greater than zero.