Question

Fie f:R-R, f(x) = -3x+2
Aflați x€R pentru care (f(2x)+4)/2 + f(-1)=f(-x)+f(2/3)

Answer 1

$f:\mathbb{R}\rightarrow\mathbb{R} \: \: \: ,f(x)=-3x+2$

$\frac{f(2x) + 4}{2} + f( - 1) = f( - x) + f( \frac{2}{3} )$

$\frac{ - 3 \times 2x + 2 + 4}{2} + ( - 3) \times ( - 1) + 2 = - 3 \times ( - x) + 2 + ( - 3) \times \frac{2}{3} + 2$

$\frac{ - 6x + 6}{2} + 3 + 2 = 3x + 2 - 2+ 2$

$\frac{6( - x + 1)}{2} +5 = 3x + 2$

$3( - x + 1) +5 = 3x + 2$

$- 3x - 3 +5 = 3x + 2$

$- 3x - 3x = 2 + 3 -5$

$- 6x = 0 \: | \div ( - 6)$

$x = 0\: \in \: \mathbb{R}$