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Let f:NrarrN be a function such x-f(x)=1...

Let `f:NrarrN` be a function such `x-f(x)=19[(x)/(19)]-90[(f(x))/(90)],AAx in N` , where [.] denotes the greatest integer function and [.] denotes the greatest integers function and `1900ltf(1990)lt2000`, then possible value of `f(1990)` is

A

`1994`

B

`1924`

C

`1954`

D

`1934`

Text Solution

Verified by Experts

The correct Answer is:
A
`1990-f (1990) = 19[(1990)/(19)]-90[f(1990)/(90)]`
`because 21.11lt f(1990)/(90)lt22.22,`
`because [f(1990)/(90)]=21,22`
`implies f(1990)=1994 or 1904`
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