If (S(x)=s-4x) and (S(2)-S(9)=28), which conclusion is correct?

Correct answer: The condition is true for every real \(s\)

\(S(2)=s-4(2)=s-8\) and \(S(9)=s-4(9)=s-36\). Therefore, \(S(2)-S(9)=(s-8)-(s-36)=28\). The terms containing \(s\) cancel, so the condition is true for every real \(s\). Neither \(s=28\) nor \(s=4\) is a specially required value. Exam tip: In differences of function values, write both values first and check whether the parameter terms cancel.