Home
Class 12
MATHS
If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1)...

If `f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):}`, where [] denotes the greatest integer function, then

A

f(x) is continuous for all `x in [0, 2)`

B

f(x) is differentiable for all `x in [0, 2) - {1}`

C

f(X) is differentiable for all `x in [0, 2)-{(1)/(2),1}`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|50 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|26 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    ARIHANT MATHS|Exercise Exercise For Session 6|5 Videos

  • COMPLEX NUMBERS

    ARIHANT MATHS|Exercise Complex Number Exercise 8|3 Videos

  • COORDINATE SYSTEM AND COORDINATES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|7 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then continutity and diffrentiability of f(x)

If f(x) = {{:("sin"(pix)/(2)",",x lt 1),([x]",",x ge 1):} , where [x] denotes the greatest integer function, then

f(x)=1/sqrt([x]^(2)-[x]-6) , where [*] denotes the greatest integer function.

If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

If f(x) =[ sin ^(-1)(sin 2x )] (where, [] denotes the greatest integer function ), then

Discuss the continuity of f(x) in [0, 2], where f(x) = {{:([cos pi x]",",x le 1),(|2x - 3|[x - 2]",",x gt 1):} where [.] denotes the greatest integral function.

Consider the function f(x) = {{:(x{x}+1",","if",0 le x lt 1),(2-{x}",","if",1 le x le 2):} , where {x} denotes the fractional part function. Which one of the following statements is not correct ?

f(x)=sin^(-1)[2x^(2)-3] , where [*] denotes the greatest integer function. Find the domain of f(x).

int_(-1)^(2)[([x])/(1+x^(2))]dx , where [.] denotes the greatest integer function, is equal to

f(x)=sin^(-1)((2-3[x])/4) , which [*] denotes the greatest integer function.