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If f:R in R is defined by f(x)=(x^(2)-...

If `f:R in R` is defined by
`f(x)=(x^(2)-ax+1)/(x^(2)+ax+1),0ltalt2`, the which of the following is true:

A

`(2 + a)^2 f'' (1) + (2 -a)^2 f'' ( -1) = 0`

B

`(2-a)^2 f'' (1) - (2 + a)^2 f'' (-1) = 0`

C

`f'(1) f' (-1) = (2 - a)^2`

D

`f'(1) f'(-1) = -(2 + a)^2)`

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Knowledge Check

  • Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2 - ax + 1)/(x^2+ax+1) ;0 lt a lt 2 . Which of the following is true?

    A
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    B
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    C
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    D
    f(x) is decreasing on (-1,1) but has neither a local maximum nor a local minimum at x=1

  • If f :R to R is defined by f (x) =(x )/(x ^(2) +1), find f (f(2))

    A
    `29/10`
    B
    `1/29`
    C
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  • If the function F: R to R is defined by f(x)=|x|(x-sinx) , then which o f the following statemnts is true ?

    A
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    C
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