Re: DSE 2009

Posted by s on Feb 22, 2012; 11:24am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2009-tp7296495p7308017.html


for 1st question, consider an increasing fn f(x)=x let x=1/2, y=1...so |f(1)-f(2)|=1/2 and |1/2-1|^3= 1/8...1/2 is not less than or equal to 1/8 so this result dint hold for an increasing fn..because if it did it must hold for all increasing functions.

consider a decreasing fn f(x)=1/x let x=1,y=2 now |f(1)-f(2)|=1/2 and |x-y|^3=1/8 and inequality doesnt hold again so its not true for decreasing functions.

consider constant fn f(x)=1 , let x=2 y=3, |f(x)-f(y)|=0 and |x-y|^3=1 which satisfies inequality and always will for any constant fn as the LHS will always be 0...

so (c)

for 2nd question f takes only rational values,if f was incr or decr given its continuous in the interval it can take irrational values for some x...only for a constant fn its guranteed that f will take a particular rational value..so f is constant thus f(2)=1 ...so (d)