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If f(x) = (x-1)/(x+1), then f(alpha, x)...

If `f(x) = (x-1)/(x+1),` then `f(alpha, x)=`

A

`(f(x)+alpha)/(1+alpha f(x))`

B

`((alpha-1)f(x) + alpha +1)/((alpha+1)f(x)+(alpha-1))`

C

`((alpha+1)f(x) +alpha-1)/((alpha-1) f(x) + (alpha+1))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
We have
`f(x) =(x-1)/(x+1)rArr (f(x) +1)/(f(x) -1) = (2x)/(-2) rArr x = (1+f(x))/(1-f(x))`
`therefore f (alphax) = (alphax -1)/(ax + 1) =(alpha {(1+f(x))/(1-f(x))}-1)/(alpha{(1+f(x))/(1-f(x))} + 1)`
`rArr f(alpha,x) =((alpha +1)f (x) + alpha -1)/((alpha -1)f(x) + alpha f(x) + alpha +1)`
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