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.

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