Question

f(x + y) = f(x)f(y) for all x, y, f(4) = + 3 what is f(–8)?
43468
43474
9
6

Answer 1

Step-by-step explanation:

The ans is 1/9.

We need to find f(-8) and try getting into - 4-4 form

Answer 2

Answer:

1/9

Step-by-step explanation:

General solution of Functional equation of the type $F(x+y)=F(x)F(y)$ is given as $\alpha ^{kx}$ where k is arbitarily constant and $\alpha$ can be any R.

Now in the given question

$f(x) = \alpha ^{kx}(say)\\f(4) = \alpha ^{4k} =3......(1)\\f(-8) = \alpha ^{-8k}=(\alpha ^{4k})^{-2}=3^{-2}=\frac{1}{9} .......from(1)$.