Q40 of 155 Page 9

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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