If \(f(x)=x^2-5x\) and \(g(x)=x\), what are the zeroes of \((f+g)(x)\)?

Correct answer: \(\{0,4\}\)

For the sum of two functions, \((f+g)(x)=f(x)+g(x)=(x^2-5x)+x=x^2-4x=x(x-4)\). Thus, the expression is zero when \(x=0\) or \(x=4\), so the correct set is \(\{0,4\}\). Option B gives the zeroes of \(f(x)\) alone, not those of \(f(x)+g(x)\). Exam tip: first form the sum of the functions and then factorise it to find its zeroes.