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How many point of discontinuity for the following function in its. domain. ,,f(x)={x|x|,if x<0-1,ifx≥0 -

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Question

How many point of discontinuity for the following function in its. domain.

`f(x) = {{:(x/|x|",", if  x < 0),(-1",", if x ≥ 0):}`

Options

  • 0

  • 1

  • 2

  • 3

MCQ

Solution

0

Explanation:

At `x` = 0, L.H.L

= `lim_(x -> 0) - (x/|x|)` = – 1

`f(0)` = – 1

R.H.L = `lim_(x -> 0^+) f(x)` = – 1

∴ L.H.L = f(0) = R.H.L

∴ `f` is continuous at `x` = 0

Also at `x` = C < 0

`lim_(x -> C) (x/|x|) = - 1 = f(c)`

∴ `lim_(x -> C) f(x) = f(c)f` is continuous at `x` = C < 0

`x -> C`,

A + `x` = c > 0, `lim_(x -> C) f(x)` = 1

`lim_(x -> C) = f(c)` ⇒ `f` is continuous at `x` = C > 0.

There is no point of discountinuity for this function in its domain.

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