f-x-2-f-x-2-f-1-1-

Question Number 860 by 123456 last updated on 28/Mar/15

f (x^{2}) = {[f (x)]}^{2}

f (1) = 1

Commented by prakash jain last updated on 28/Mar/15

f (x) = 0 or f (x) = 1

f (x) = x^{k}, k \in R

Answered by prakash jain last updated on 28/Mar/15

f (x^{2}) = f (x) \cdot f (x)

divide by x^{2}

\frac{f (x \cdot x)}{x \cdot x} = \frac{f (x)}{x} \cdot \frac{f (x)}{x}

g (x) = \frac{f (x)}{x}

If g (x y) = g (x) g (y) \Rightarrow g (x) = x^{k}, k \in R

hence

f (x) = x^{k}, k \in R