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Question

If y=1t2+t2 where t=1x1, then which of the following is/are true about continuity of y=f(x) in R?

A
f(x) is discontinuous at x=12
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B
f(x) is continuous at x=1
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C
f(x) is discontinuous at x=2
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D
f(x) is continuous at x=12
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Solution

The correct option is C f(x) is discontinuous at x=2
Given: y=1t2+t2, t=1x1
Now,
y=f(x) will be discontinuous where t is discontinuous i.e. at x=1
Also, when
(t+2)(t1)=0t=2,11x1=2,1x=12,2
Hence, y=f(x) is discontinuous at x=12,1,2

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