Question

1 + x
10. Prove that the function f(x) = Log
satisfies the equation
1-X
X1 + X2
f(x1) + f(x2) = f
1 + X1 X2 )​

Answer 1

Answer:

Correct option is

C

f(x)+f(y)=f(

1+xy

x+y

)

Since, f(x)=log(

1−x

1+x

)

∴f(

1+xy

x+y

)=log(

1−

1+xy

x+y

1+

1+xy

x+y

)

=log(

1+xy−x−y

1+xy+x+y

)

Now, f(x)+f(y)=log(

1−x

1+x

)+log(

1−y

1+y

)

=log(

(1−x)(1−y)

(1+x)(1+y)

)

=log(

1+xy−x−y

1+x+y+xy

)

∴f(

1+xy

x+y

)=f(x)+f(y)