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Let f(1)(x) = x/(x+1) AA x in R^(+), se ...

Let `f_(1)(x) = x/(x+1) AA x in R^(+)`, se of positive real numbers, For `k ge 2`, define
`f_(k)(x) = f_(k-1)(f_(1)(x)) AA x in R^(+)`
Then `f_(2020)(1/2020)` is equal to

A

`1/(4040)`

B

`1/(2020)`

C

`1/(4041)`

D

`1/(2021)`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • Let f: N to N be defined by f(x) = x-(1)^(x) AA x in N , Then f is

    A
    one-to-one but not onto
    B
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    C
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  • If f (x) +2f (1 - x) = x^2 +2 AA x in R then f (x) is equal to

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    `x^2 -2`
    B
    `1`
    C
    `1/3 (x-2)^2`
    D
    None of these

  • If f: R to R be defined by f(x) =(1)/(x), AA x in R. Then , f is

    A
    one-one
    B
    onto
    C
    bijective
    D
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