Let f(x) f(y)=f(x y) for all real x, y . If f(2)=4 , then what is the value of f ( 1 2 ) ?

Step-by-step solution

Given f(x)=f(y) Let f ( x )= x ^ n and f ( y )= y ^ n . aligned & f ( xy )=( x y )^ n & f (2)=4 4=(2)^ n n =2 & f ( xy )=( xy )^2 & f ( 1 2 )= ( 1 2 )^2= 1 4 aligned