Find all point of discontinuity of the function `f(t)=1/(t^2+t-2),` where `t=1/(x-1)`

Answer

Hence points at which` f(t) `is discontinuous are `x={1 / 2,1,2}`

At all other point it is continuous.

Explanation

ATQ,

`t=\frac{1}{x-1}` is discontinuous at` x=1` as ` t` is not defined at this point.


`\therefore f(t)` being a composition of function involving t, it is also discontinuous at ` x=1`



` f(t)=\frac{1}{t^{2}+t-2}`

`=\frac{1}{(t+2)(t-1)}`



we can say that` f(t)` is not defined at


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