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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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