Book: RD Sharma - Mathematics (Volume 1)
Chapter: 9. Continuity
Subject: Maths - Class 12th
Q. No. 19 of Exercise 9.2
Listen NCERT Audio Books to boost your productivity and retention power by 2X.
19
Find all point of discontinuity of the function 
where 
Clearly,
is discontinuous at x = 1 as t is not defined at this point.
∴ f(t) being a composition of function involving t, it is also discontinuous at x = 1
∵ 
by observing f(t) we can say that f(t) is not defined at
t = – 2 and t = 1.
∴ this will also contribute to discontinuity
Hence,
⇒ x – 1 = –1/2
⇒ x = 1 – 1/2
⇒ x = 1/2
also other point of discontinuity is obtained by :
⇒ x – 1 = 1
⇒ x = 2
Hence points at which f(t) is discontinuous are x = { 1/2,1,2}
At all other point it is continuous.
