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If f(x)=log((1+x)/(1-x)),t h e n (a)f(...

If `f(x)=log((1+x)/(1-x)),t h e n` (a)`f(x_1)f(x_2)=f(x_1+x_2)` (b)`f(x+2)-2f(x+1)+f(x)=0` (c)`f(x)+f(x+1)=f(x^2+x)` (d)`f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))`

A

`f(x_(1))*f(x_(2))=f(x_(1)+x_(2))`

B

`f(x+2)-2f(x+1)+f(x)=0`

C

`f(x)+f(x+1)=f(x^(2)+x)`

D

`f(x_(1))+f(x_(2)) = f ((x_(1)+x_(2))/(1+x_(1)x_(2)))`

Text Solution

Verified by Experts

The correct Answer is:
D
` f(x_(1)) + f(x_(2)) = log ((1+x_(1))/(1- x_(1))*(1+x_(2))/(1-x_(2)))`
`= log((1+x_(1)x_(2)+x_(1)+x_(2))/(1+x_(1)x_(2)-x_(1)-x_(2)))`
`= log((1+(x_(1)+x_(2))/(1+x_(1)x_(2)))/(1-(x_(1)+x_(2))/(1+x_(1)x_(2))))= f ((x_(1)+x_(2))/(1+x_(1)x_(2)))`
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CENGAGE PUBLICATION-LOGARITHM AND ITS PROPERTIES-Exercises (Single Correct Answer Type)
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