Let f(x)={2/(1+x^2),xi sr a t ion a l b ...

Let `f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l` has exactly two points of continuity then the value of `b` are `(0,3]` b. `[0,1]` c. `(0,2]` d.`varphi`

`x AA x in R`

`f(x)={(x",",x" is irrational"),(1-x",",x" is rational"):}`

`f(x)={(x",",x" is rational"),(1-x",",x" is irrational"):}`

None of these

Text Solution

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The correct Answer is:

`f(f(x))={(f(x)",",f(x)" is rational"),(1-f(x)",",f(x)" is irrational"):}`
`f(x)={(x",",x" is rational"),(1-(1-x)=x",",x" is irrational"):}`.

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