Continuous or Discontinuous ??

f(x) = x - l x - x² l

x Îµ [ -1 , 1]

Then the no of points at which f(x) is discontinuos

(A) 2

(B) 1

(D) None

2 Answers

Let us construct the function .

f ( x ) = x ² , whenever x â‰¥ x ² , i . e , whenever x lies between 0 to 1 .

= 2x - x ² , whenever x â‰¤ x ² , i . e , whenever x lies between - 1 to 0 .

Clearly , x = 0 is the only critical point .

But , both the R . H . L and L . H . L have the same value as the functional value at x = 0 ,

i.e , both are zero at x = 0 .

So the function has zero number of discontinuities .

Thanks

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