Question

Fie f:R>R,f(1-2x)=2x+11-f(3).Calculati f(3)+f(-3)

Answer 1

$y->1-2x=>x=\frac{1-y}{2} \\f(y)=2(\frac{1-y}{2})+11-f(3)=1-y+11-f(3)=12-y-f(3) \\f(x)=12-x-f(3)\\f(3)=12-3-f(3)<=>2f(3)=9=>f(3)=\frac{9}{2}\\ f(-3)=12+3-f(3)=15-\frac{9}{2}=\frac{30-9}{2}=\frac{21}{2}\\ f(3)+f(-3)=\frac{9}{2}+\frac{21}{2}=\frac{30}{2}=15\\ f(3)+f(-3)=15$