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| + |x – 1| at x = 0, 1.
To prove whether f(x) is continuous at x = 0 & 1
If f(x) to be continuous at x = 0,we have to show that f(0)–=f(0) + = f(0)
LHL = f(0)– = 
⇒ |(–0)| + |(–0)–1|
∴–|x| = |x| = x
⇒ |–1|
⇒ 1 ...(1)
RHL = f(0) + = 
⇒ |0| + |0–1|
∴–|x| = |x| = x
⇒ |–1|
⇒ 1 ...(2)
From (1) & (2),we get f(0)–=f(0) +
Hence ,f(x) is continuous at x = 0
If f(x) to be continuous at x = 1,we have to show, f(1)– =f(1) + = f(1)
LHL = f(1)– = 
⇒ |(1–0) + (–0)|
⇒ |(1)|
⇒ 1 ...(3)
RHL = f(1) + = 
⇒ |(1 + 0)| + |0|
∴–|x| = |x| = x
⇒ |1|
⇒ 1 ...(4)
From (3) & (4),we get f(1)– = f(1) +
Hence ,f(x) is continuous at x = 1
