Prove that is discontinuous at

x = 0.

Given:

f(0) = 2

we have to prove that f(x) is discontinuous at x = 0

If f(x) to be discontinuous at x = 0,then

LHL = f(0)^{–} =

|–x| = |x| = x

⇒ 2 ...(1)

RHL = f(0) ^{+} _{=}

⇒ 0 ...(2)

From (1) & (2),we know that,

f(0)^{–} f(0) ^{+}

Hence, f(x) is discontinuous at x = 0

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