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Statement -1 : y = [x] , ([.] denotes gr...

Statement -1 : y = [x] , ([.] denotes greatest integer function) is not a continuous function .
Statement -2 : {x} ({.} denotes fractional fractional function) is discontinuous at integral points.
Statement -3 : ` y = 7^(x)` is continuous in its domain.

A

TFT

B

TTT

C

FFF

D

FFT

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • The function f(x) =[x] cos{(2x-1)//2} pi denotes the greatest integer function, is discontinuous at:

    A
    all x
    B
    all integer points
    C
    no x
    D
    x whixh is not an integer

  • If f(x) = [x^(-2) [x^(2)]] , (where [*] denotes the greatest integer function) x ne 0 , then incorrect statement

    A
    f(x) is continuous everywhere
    B
    f(x) is discontinuous at `x = sqrt(2)`
    C
    f(x) is non-differentiable at x = 1
    D
    f(x) is discontinuous at infinitely many points

  • The function f(x)={x} sin (pi[x]) , where [.] denotes the greatest integer function and {.} is the fractional part function, is discontinuous at

    A
    all x
    B
    all integer points
    C
    no x
    D
    x which is not an integer