Given-f-x-y-4f-x-f-y-for-all-real-numbers-x-and-y-If-f-3-32-then-f-1-

Question Number 119815 by bemath last updated on 27/Oct/20

G i v e n f (x + y) = 4 f (x) . f (y) f o r

a l l r e a l n u m b e r s x a n d y .

I f f (3) = 32 t h e n f (1) =_

Answered by Olaf last updated on 27/Oct/20

f (1 + 1) = 4 f (1) f (1)

f (2) = 4 f {(1)}^{2}

f (2 + 1) = 4 f (2) f (1)

f (3) = 16 f {(1)}^{3} = 32

f (1) = \sqrt[3]{2}

Commented by bemath last updated on 27/Oct/20

y e s \dots .

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