Q. 39 B5.0( 1 Vote )

Discuss the continuity of the f(x) at the indicated points :

f(x) = |x – 1| + |x + 1| at x = – 1, 1.

Answer :

To prove whether f(x) is continuous at –1 & 1


If f(x) to be continuous at x = –1,we have to show, f(–1)=f(–1) + =f(–1)


LHL = f(–1) =




|(–2–0)| + |–0|


|–2|


|–x| = |x| = x


2 ...(1)


RHL = f(–1) + =




|(–2 + 0)| + |0|


|–x| = |x| = x


|–2|


2 ...(2)


From (1) & (2),we get f(–1)=f(–1) +


Hence ,f(x) is continuous at x = –1


If f(x) to be continuous at x = 1,we have to show, f(1) =f(1) + =f(1)


LHL = f(1) =




|–0| + |2–0|


|2|


2 ...(3)


RHL = f(1) + =




|0| + |2 + 0|


|–x| = |x| = x


|2|


2 ...(4)


From (3) & (4),we get f(1)=f(1) +


Hence ,f(x) is continuous at x = 1


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