Points of Continuity

[Amit Goyal]

 Let f(x) be the function defined on the interval (0, 1) by 
    f(x) = x(1-x) if x is rational 
               1/4 - x(1-x) if x is irrational 

Then f is continuous 
(a) at no point in (0, 1) 
(b) at exactly one point in (0, 1) 
(c) at exactly two points in (0, 1) 
(d) at more than two points in (0, 1) 

[harmeet bhatia]

i think its a. :)

[Suruchi Sawhney]

i think its (b).
There exists one point in (0,1) for which the function is continuous

[harmeet bhatia]

hi suruchi, can you plz explain your procedure?

[Srishti Gupta]

i think its a

[Suruchi Sawhney]

I solved it using sequential approach to continuity.

If we solve the equation : x(1-x) = 1/4 - x(1-x) , we get one value of x which lies in (0,1)
So the function will be continuous at that point as the f(sequence of rationals) will converge to f(irrational) and vice versa .

How did u get (a) ?

[Pankhuri Jha]

a was my guess too

though i'm not too sure

On Saturday, June 2, 2012 10:31:53 AM UTC+5:30, Srishti Gupta wrote:

i think its a

[Divya Singh]

I agree with suruchi. Even I am getting continuous at one point.

[harmeet bhatia]

i did in the same way as you suruchi but  didn't get any value of x from this equation.. may be some calculation error. i'll check again. :)

[akshay bhatnagar]

b at x=1/root(2) it is continuous

[akshay bhatnagar]

AS ORDERED AND SHOWN BY Ms. Prerna Rakheja  you are great  
.roots is not 1/root(2)
ans is
C as both roots lie between (0,1)
MY GRACE 

[Prerna Rakheja]

Akshay :@ :@ :@

On Saturday, June 2, 2012 11:06:00 AM UTC+5:30, akshay bhatnagar wrote:

AS ORDERED AND SHOWN BY Ms. Prerna Rakheja  you are great  
.roots is not 1/root(2)
ans is
C as both roots lie between (0,1)
MY GRACE 

[Bhavika Nanawati]

Are the two roots ;

1/2 + 1/ [ 2*sqrt(2)] and  1/2 - 1/ [ 2*sqrt(2)] ?

yes, the answer is (c) I think.

[Prerna Rakheja]

Yes Bhavika these are the two roots. : )

[Srishti Gupta]

yess my mistake..same as bhavika..prernaa :):) answer is c :P

[Suruchi Sawhney]

Yes, there are two roots as shown