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1 solution
f ( x ) > 0,So f ( f ( x ) ) > 0 ,So f ′ ( x ) > 0 ,Hence f(x) is an increasing function.Now apply mean value theorem, f ′ ( c ) = a f ( a ) − f ( 0 ) for some c in between (a,0),a(f(f(c)))=f(a)-f(0).Now since f(x) is increasing,it is very easy to conclude that f(0)<f(f(c)).Plug this in the previous equation and u get f(a)<(a+1)f(f(c))...So any contradiction?????What if a=(-5)...think it is almost done....Hope u liked the problem....For getting more such problems go on upvoting me...XD.. :P