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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`

A

(0,3]

B

[0,1]

C

(0,2]

D

`phi`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)={{:((2)/(1+x^(2))",","x is irrational"),(b",","x is rational"):}` has exactly two points of continuity then equation `(2)/(1+x^(2))=b` must have two distinct roots.
Now `(2)/(1+x^(2)) in(0,2]`
`rArr" "b in {0,2]`
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