Its a Function!

Algebra Level pending

For a real valued function \( f(x) \) satisfying [ 2f(xy) = \( (f(x))^{y} \) + \( (f(y))^{x} \) ] for all x , y \( \epsilon\) \( \mathbb R\) and \( f(1) \) = a , ( a \( \neq \) 1 ). Then what is the value of the expression \[ [(a-1) . \displaystyle\sum_{i=1}^n f(i)] + a \] .

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