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If f(x)=(x^2-1)/(x^2+1) . For every real...

If `f(x)=(x^2-1)/(x^2+1)` . For every real number `x ,` then the minimum value of `fdot` does not exist because `f` is unbounded is not attained even through `f` is bounded is equal to 1 is equal to `-1`

A

does not exist because `f ` is unbounded

B

is not attained even through `f` is bounded

C

is 1

D

is `-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, ` f(x) = (x ^(2) - 1)/( x ^(2) + 1) = 1 - ( 2)/( x ^(2) + 1)`
`f(x)` will be minimum, when ` (2)/(x ^(2) + 1)` is maximum,
i.e., when `x ^(2) + 1 ` is minimum.
i.e., at ` x = 0`
`therefore ` Minimum value of ` f (x) ` is `f (0) = -1 `
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