Question

prove that f(x) .f(1/x) = f(x) +f(1/x)​

Answer 1

Answer:

f(x)+f(

x

1

)=0 is satisfied by f(x)=klnx, where k is a constant.

Given that f(e)=1⇒k=1

f(x)=lnx

⇒f

−1

x=e

x

⇒g(x)=e

x

⇒g

′

(x)=e

x