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

$$Givenf(x+y)=4f\left(x\right).f\left(y\right)for$$$$allrealnumbersxandy.$$$$Iff\left(3\right)=32thenf\left(1\right)=\mathrm{\_}$$

Answered by Olaf last updated on 27/Oct/20

$$f(1+1)=4f\left(1\right)f\left(1\right)$$$$f\left(2\right)=4f{\left(1\right)}^2$$$$$$$$f(2+1)=4f\left(2\right)f\left(1\right)$$$$f\left(3\right)=16f{\left(1\right)}^3=32$$$$f\left(1\right)=\sqrt[3]{2}$$$$$$

Commented by bemath last updated on 27/Oct/20

$$yes....$$

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