If f(1) = 1, f(2) = 2, f(3) = 3 and f(4) = 16, then determine f(5).

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[@danielbranscombe6662]

the more complete solution would use
f(x)=g(x)*(x-1)(x-2)(x-3)+x
for some polynomial g(x)
f(4)=16 gives
6g(4)+4=16
thus
g(4)=2
and that is all we can deduce about g(x) with the given information.
Since we cannot uniquely determine g(x) then we cannot uniquely determine f(5)

[@armyboy8547]

Find f(x) given that
f(0)+f(1)=3
f(2)+f(3)=20 then find f(6)?

[@randomfury7136]

Thanks

[@dipanshupanda6581]

Thank you

[@mechnovashia]

Welcome Dipanshu ☺️☺️

[@gurvatinshjjsingh6386]

7th to all mylovely teachers