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.

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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