Question

Uma função f: R⇒R é definida pela lei f(x) = -3x+5 Determine os valores de α∈R tais que: f(α) + f(α+1) = 3· f(2a)

Answer 1

$f(a)+f(a+1)~=~3.f(2a)\\\\\\(-3.(a)+5)~+~(-3.(a+1)+5)~=~3.(-3.(2a)+5)\\\\\\(-3a+5)~+~(-3a-3+5)~=~3.(-6a+5)\\\\\\-3a+5-3a+2~=~-18a+15\\\\\\-3a-3a+18a~=~15-5-2\\\\\\12a~=~8\\\\\\a~=~\frac{8}{12}\\\\\\\boxed{a~=~\frac{2}{3}}$