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If a function y=f(x) is defined as y=(1)...

If a function y=f(x) is defined as `y=(1)/(t^(2)-t-6)and t=(1)/(x-2), t in R`
Then, f(x) is discontinuous at

A

`2,(2)/(3),(7)/(3)`

B

`2,(3)/(2),(7)/(3)`

C

`2,(3)/(2),(5)/(3)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
We observe that t is not defined at x=2 and y is not defined at t=-2,3
`t=-2 Rightarrow x=(3)/(2) and t=3 Rightarrow x=(7)/(3)`
Hence, f(x) is continuous at x=`2,(3)/(2) and (7)/(3)`
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