f(0)=1

as per question substitute y=0 to get above result

now when u substitue y=-x

f(2x)=f(x)f(-x)

Put x=x/2

f(x)=f(x/2)f(-x/2)

and f(-x)=f(-x/2)f(x/2)

HENCE EVEN FUNCTION

GOOD QUESTION BOSS!