IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

jovien09

the domain of derivative of the function

f(x)= , if |x| 1

1/2 (|x|-1), if |x| > 1

a) R - {0}

b) R - {1}

c)R - { -1}

d) R - { -1, 1}

apurviitjee2008

are u sure about the options?
plz chck them
its R i think

asish

is it r(not in options though )

apurviitjee2008

plz give the second part of the qs clearly
its not clear whether the part |x|-1 is in num or denom

vaibhavbright

ans. is B) given dat (|x|-1) is in D^r

sawasthi

@Vaibhav,

Answer would be (D) if (|x| - 1) would be in denominator and not B, as even at -1, it would not be defined..

if it is in Numerator it would be R ( which is not in Options Given)

Please find the attached Graphical plot of the differential..although domain is Entire R, but.differential is not defined at -1,1

jovien09

(|x|-1) is in the numerator

asish

then ans is r

apurviitjee2008

@sawasthi plz check the value of the function at -1

sawasthi

@apurviitjee2008

it is perfect ...

At -1, from Left side it is approaching 1/2 but Open interval

from Right side, it is 0 ( closed interval)

f ' (-1) = 1/2 * (|-1| - 1) = 1/2*(1-1) = 0

Answer would be Entire R...for Domain

apurviitjee2008

agree with u ans is r

(was saying about ur prev ans )