Oxford Entrance Exam Problem 6

The functions \(S\) and \(T\) are defined for real numbers by

\(S(x)=x+1\) and \(T(x)=-x\).

The function \(S\) is applied \(s\) times and the function \(T\) is applied \(t\) times, in some order, to produce the function

\(F(x)=8-x\).

It is possible to deduce that

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