Let f:R-R be a continuous function such that f(3x)-f(x)=x. If f(8)=7, then f(14) is equal to:

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Let f:R-R be a continuous function such that f(3x)-f(x)=x. If f(8)=7, then f(14) is equal to:
A. 4
B. 10
C. 11
D. 16

MaThrick Masterji

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Simpler would be to just let g(x)=f(x)-x/2 so that g(3x)=g(x) and note that g must be constant over [1, 3) since otherwise lim_(x-->0) g(x) cannot exist. But then g must be constant, so you find f(x)=x/2+3, and hence f(14)=10.

LipschitzHutchinson

I am facing great difficulty in functional equation questions and no of functions type ques any tips ??

seema

I found out the value of f(24) which was 15. Then I thought that since f(24)=15, f(14) has to be definitely less than 15 so the options left are 10 and 11. I then saw that f(8)=7 and since there is a huge gap between 14 and 24, I guessed that the answer would be the lesser of the two i.e 10.
Would that be a correct assumption to make

Shogun

Why are we taking lim n tending to infinity?

mehulsahai

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