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

Options

A. `2,(2)/(3),(7)/(3)`
B. `2,(3)/(2),(7)/(3)`
C. `2,(2)/(3),(7)/(3)`
D. none of these

Answer

B

Explanation

We have
`y=(1)/(t^(2)-t-6)=(1)/((t-3)(t+2)) and ,t=(1)/(x-2)`
We observe that t is not defined at x=2 and y is not defined at t=-2,3
Now,
`t=-2 Rightarrow -2=(1)/(x-2) Rightarrow x=(3)/(2)`
`and t=3 Rightarrow 3=(1)/(x-2) Rightarrow x=(7)/(3)`