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Solve the following problems from (i) to (v) on functional equation. (i) The function f(x) defined on the real numbers has the property that f(f(x)) . (1 + f(x)) = –f(x) for all x in the domain of f. If the number 3 is the domain and range off, compute the value of f(3). (ii) Suppose f is a real function satisfying f(x + f(x)) = 4f(x) and f(1) = 4. Find the value of f(21). (iii) Let 'f' be a function defined from R^(+) to R^(+) . [f(xy)]^(2) = x (f(y))^(2) for all positive numbers x and y and f (2) = 6 , find the value of f (50) . (iv) Let f(x) be a function with two properties (a) for any two real number x and y, f(x + y)= x + f(y) and (b) f(0) = 2. Find the value of f(100). (v) Let f(x) be function such that f(3) = 1 and f(3x) = x + f(3x – 3) for all x. Then find the value of f(300).

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Answer :(i) `(-3)/4`(ii) 64(III) 30(iv) 102(v)5050


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