ISI MSQE prev year question

Posted by XIPP on Dec 03, 2013; 5:29pm
URL: http://discussion-forum.276.s1.nabble.com/ISI-MSQE-prev-year-question-tp7584297.html

SEE isi 2007 msqe paper, q26 of math section.

Suppose the real valued continuous function f defined on the set of non-negative real
numbers satisfies the condition f(x) = xf(x), then f(2) equals
a:1,
b:2,
c:3,
d:f(1)


And I can see by elimination that f(2)=2*f(2) condition is not satisfied for f(2)=1,2,3 and so f(1) should be answer. But, how is f(1) really the answer? that is how f(1) can be derived if I don't follow the method of elimination?