Re: Discussion Problem_(11)

Posted by Sinistral on May 23, 2013; 3:15pm
URL: http://discussion-forum.276.s1.nabble.com/Discussion-Problem-11-tp7581175p7581183.html

Sumit wrote

Now, If we take f(x)=X^2 then F(1)=1 n F(0)=0....also If we put irrational no square root of 2 in this function
we will get a rational no.
So, the answer is a) 0.

in ur above definition take x to be cube root of 2, this function f(x) again will give an irrational number. hence option a also discarded.

basically u r ignoring the condition that f(x) is continuous for all x & f(x) is rational for all x. so f(x) has to be a constant function. since f(1) is given to be 1 ==> f(x)=1.
hence option (b)

PS: the concepts underlying these kind of questions were discussed in detail by Amit Sir in one of the threads a few days back.