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Question 14

The function $$f$$ satisfies $$f(f(x))=f(x+2)-3$$ for all integers $$x$$. If $$f(1)=4$$ and $$f(4)=3$$, then $$f(5)$$ equals

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Put $$x=1$$ to get $$f(4)=f(3)-3$$, so $$f(3)=6$$. Put $$x=4$$ to get $$f(3)=f(6)-3$$, giving $$f(6)=9$$. Finally, putting $$x=3$$ gives $$f(6)=f(5)-3$$, so $$f(5)=12$$.

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