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For xinR-{10,1}, " let " f1(x)=1/x,f2(x)...

For `xinR-{10,1}, " let " f_1(x)=1/x,f_2(x)=1-x" and "f_(3)(x)=1/(1-x)` be three given fuctions. If a function J(x) satisfies `(f_2oJof_1)(x)=f_3(x)`, then J(x) is equal to

A

`f_(2)(x)`

B

`1/2f_(3)(x)`

C

`f_(1)(x)`

D

`f_(3)(x)`

Text Solution

Verified by Experts

The correct Answer is:
D
`1/(1-x)=1-J.f_(1)(x)implies1.(1-x)=1-J(1/x)impliesJ(1/x)=(-x)/(1-x)=1/(1-1/x)impliesJ(x)=1/(1-x)=f_(3)(x)`
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