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Let f and g be functions satisfying f(x + y) = f(x)f(y), f(1) = 7 and g(x + y) = g(xy), g(1) = 1, for all x, y N. If x = 1n ( f(x)g(x) ) = 19607, then n is equal to :
(4) 5
f(x + y) = f(x)f(y), f(1) = 7 f(x) = 7x for x N
g(x + 1) = g(x 1) = g(x) ⇒ g is constant on N ⇒ g(x) = g(1) = 1
x = 1n 7x = 7(7n - 1)6 = 19607
7n - 1 = 16806 7n = 16807 = 75
n = 5
Answer: (4)
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