#Algebra-2

f(x+y)=f(x)*f(y) for al x and y. f(4) = 3,then what is the value of f(-8)?

Solution-

f(4) = 3
=>f(2+2) = f(2)*f(2)
=>3 = f(2)^2
=>±√3 = f(2)----------(1)

Now, f(2) =  f(4-2)
=> f(4 - 2) = f(4)*f(-2)
=>±√3 = 3*f(-2)
=>f(-2) = ±1/√3------(2)

f(-8) = f(-4 - 4) = f(-4)*f(-4)
and, f(-4) = f(-2-2) = f(-2)*f(-2)
So, f(-8) = f(-2)*f(-2)*f(-2)*f(-2)
       f(-8) = f(-2)^4 = (1/√3)^4
       f(-8) = 1/9 ANS

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