f is defined in [ -5 , 5 ] as

  • Option 1)

    f(x)\; is \; continuous\; at\; every\; x,except\; x=0

  • Option 2)

    f(x)\; is \; discontinuous\; at\; every\; x,except\; x=0

  • Option 3)

    f(x)\; is \; continuous\; everywhere

  • Option 4)

    f(x)\; is \; discontinuous\; everywhere

 

Answers (1)
V Vakul

As we learnt in 

Condition for discontinuity -

1. \:L\neq R

\lim_{x\rightarrow a^{-}}\:f(x)=\lim_{x\rightarrow a^{+}}\:f(x)

limit of function at x = a does not exist.

2.\:L=R\neq V

limit exist but not equal to  x = a

-

f(x)=\left\{\begin{matrix} x& x\ is\ rational\\ -x& x\ is\ irrational \end{matrix}\right.

ab x=0 both  are 0 so thas

f\left (x \right ) is continuous at  x=0

 


Option 1)

f(x)\; is \; continuous\; at\; every\; x,except\; x=0

Incorrect
 

Option 2)

f(x)\; is \; discontinuous\; at\; every\; x,except\; x=0

Correct

Option 3)

f(x)\; is \; continuous\; everywhere

Incorrect
 

Option 4)

f(x)\; is \; discontinuous\; everywhere

Incorrect
 

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