Question

let f(x) be a function satisfying f(x)f(y)=f(xy) for all real x,y . If f(2) = 4 ,then what is the value of f(1/2)?

Answer 1

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Answer 2

substitute x=y=1 :
f(1)*f(1)-f(1)=0
f(1)=0 or f(1) =1 ----------> [1]
substitute x=2 :
f(2)*f(1/2)=f(1);
f(1/2)=f(1) / 4 = either 0 or 1/4

Answer 3

but f(2)f(1)=f(2)
f(1)=1 --- > [2]
hence, the only answer is f(1/2) = 1/4