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Discuss the continuity of the function f...

Discuss the continuity of the function f, where f is defined by`f(x)={{:(-2, ifxlt=-1),( 2x , if-1 < x lt= 1),( 2, ifx >1):}`

Text Solution

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Here, value of `f(x)` is changing at `x = 1` and `x = -1`.
So, `f(x)` to be continuous,
`f(-1^-) = f(-1^+)`
`=>-2 = 2(-1)`
`=>-2 = -2`, which is true.
`:. L.H.L. = R.H.L.`
So, `f(x)` is continuous at `x = -1`.
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