Question

A função F de R é tal que, para todo x �R, F(3x) = 3.F(x). Se F(9) = 45, calcule F(1).

Answer 1

$3.F(x)=F(3x)\\\\3.F(1)=F(3)\\\\F(1)=\frac{F(3)}{3}\\\\\\3.F(3)=F(9)\\\\F(3)=\frac{F(9)}{3}\\\\F(3)=\frac{45}{3}\\\\F(3)=15\\\\\\F(1)=\frac{F(3)}{3}\\\\F(1)=\frac{15}{3}\\\\F(1)=5$