Book: RD Sharma - Mathematics (Volume 1)
Chapter: 9. Continuity
Subject: Maths - Class 12th
Q. No. 39 of Exercise 9.1
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39
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
