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Consider function f: R - {-1,1}-> R. f(x...

Consider function `f: R - {-1,1}-> R`. `f(x)=x/[1-|x|]` Then the incorrect statement is

Text Solution

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Here, `f(x) = x/(1-|x|)`
If we check `f(0^+)`, it is `0`.
Also, `f(0^-)` is `0`.
`:. f(x)` is continuous at origin.
So, statement `A` is true.

Now, `f'(0^-) =Lim_(h->0) (f(0-h)-f(0))/(0-h) = (-h/(1-h)-0)/(-h) = 1`
`f'(0^+) =Lim_(h->0) (f(0+h)-f(0))/(0+h) = (h/(1-h)-0)/(h) = 1`
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