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Which one of the following is correct in...

Which one of the following is correct in respect of the function `f(x)=(x^(2))/(|x|)" for "xne0andf(0)=0`

A

f(x) is discontinuous every where

B

f(x)= is continuous every where

C

f(x) is continuous at x=0 only

D

f(x) is discontinuous at x=0 only

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)={{:((x^(2))/(x)",",xne0),(0,x=0):}`
`={{:((x^(2))/(x)=x",",xgt0),(0",",x=0),(x^(2)/(-x)=-x",",xlt0):}`
Now, `underset(xto0)limf(x)=underset(xto0)lim(-x)=0`
`underset(xto0)limf(x)=underset(xto0)lim(x)=0`
and f(0)=0
So, f(x) is continuous for all other values of x.
Hence, f(x) is continuous everywhere.
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Knowledge Check

  • Which one of the following is correct in respect of the function f(x)=(x^(2))/(|x|) for xne0 and f(0)=0 ?

    A
    f(x) is discontinuous everywhere
    B
    f(x) is continuous everywhere
    C
    f(x) is continuous at x = 0 only
    D
    f(x) is discontinuous at x = 0 only

  • Consider the following statements in respect of the function f(x)=sin((1)/(x)) for xne0 and f(0)=0 1. underset(xrarr0)lim f(x) exists 2. f(x) is continuous at x = 0 Which of the above statements is/are correct?

    A
    A) 1 only
    B
    B) 2 only
    C
    C) Both 1 and 2
    D
    D) Neither 1 nor 2

  • Which one the following graph represents the function f(x)=(x)/(x),xne0 ?

    A
    B
    C
    D
    None of the above

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