Re: DSE 2009

Posted by ritu on Feb 26, 2012; 1:07pm
URL: http://discussion-forum.276.s1.nabble.com/DSE-2009-tp7296495p7319204.html

yar vasudha...see visualize a function f as it is defined,
initially a 45 degree line to say x=1/3,then f(x) staying constant at 1/3,nd then increasing again from x=3/4 till it reaches the point 1,1....

ie...f(x)=x when x belongs to [0,1/3)
            1/3 when x belongs to [1/3,3/4)
            8x-5/3 when x belongs to [3/4,1]

this satisfies f(0)=0 and f(1)=1,its continous and not decreasing anywhere...
now till x=1/3 g(x)=0 ...then from there onwards it wud be constant at 1/3 and then increasing till1....though it wud not be continuous in this case it wud still be non decreasing(its a step function kind) so a is also possible....and as you said b is completely true....continuity of g means f is strictly increasing....so answer is d....:)