Q13/114) Given f(x)=anx^n+an−1x^(n−1)+⋯+a1x+a0, where a0,aa,⋯,an are all smaller than 4 and not –ve Given that f(4)=2009, find f(1).

as no coefficient is >4 and we are given f(4) subtract the highest power of 4 as many times as it can go

f(4) =  1024 + 3 * 256 + 3 * 64 + 16 + 8 + 1 so

f(x) = x^5 + 3x^4 + 3x^3 + x^2 +2x +1
so f(1) = 11