Let f:R→R be a function satisfying the
functional relation
(f(x))^y +(f(y))^x =2f(xy)
for all x, y ∈R and it is given that f(1)=1/2. Answer
the following questions.
(i) f(x+y)=
(A) f(x)+f(y) (B) f(x)f(y)
(C) f(x^y y^x ) (D) ((f(x))/(f(y)))
(ii) f(xy)=
(A) f(x)f(y) (B) f(x)+f(y)
(C) (f(x))^y (D) (f(xy))^(xy)
(iii) Σ_(k=0) ^∞ f(k)=
(A) 5/2 (B) 3/2 (C) 3 (D) 2