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If f(x)=(x)/(x-1),xne1, then underset(19...

If `f(x)=(x)/(x-1),xne1`, then `underset(19" times")(ubrace(("fofo...of")(x)))` is equal to

A

`(x)/(x-1)`

B

`((x)/(x-1))^(19)`

C

`(19x)/(x-1)`

D

x

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `f(x)=(x)/(x-1)`, where `xne1`
`:." "(fof)x=f((x)/(x-1))=((x)/(x-1))/(((x)/(x-1))-1)=x`
`implies" "("fofof")x=f("fof")x=f(x)=(x)/(x-1)`
`:.("fofof...19 times")(x)=(x)/(x-1)`
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