[tex]2)\\ \\ f(x)+2f(3-x)=x \\ 2f(3-x) = x-f(x) \\ f(3-x) = \dfrac{x-f(x)}{2}\quad (1) \\ \\ f(x)+2f(3-x)=x \\ f(x) = x-2f(3-x) \quad (\text{Facem: }x\rightarrow 3-x) \\ \Rightarrow f(3-x) = (3-x) - 2f\Big(3-(3-x)\Big) \\ f(3-x) = 3-x-2f(x)\quad (2) \\ \\ \text{Din (1) si (2) } \Rightarrow \\ \\ \dfrac{x-f(x)}{2} = 3-x-2f(x) \\ x-f(x) = 6-2x-4f(x) \\ 3f(x) = 6-3x \\ \boxed{f(x) = -x+2}[/tex][tex]g(x)+3g(2-x)=x+1 \\ 3g(2-x) = x+1-g(x) \\ g(2-x) = \dfrac{x+1-g(x)}{3} \quad (1)\\ \\ g(x)+3g(2-x)=x+1 \\ g(x) = x+1-3g(2-x) \quad (\text{Facem: }x \rightarrow 2-x) \\ g(2-x) = (2-x)+1 -3g\Big(2-(2-x)\Big) \\ g(2-x) = -x+3-3g(x)\quad (2) \\ \\ \text{Din (1) si (2) } \Rightarrow \\ \\ \dfrac{x+1-g(x)}{3} = -x+3-3g(x) \\ x+1-g(x) = -3x+9-9g(x) \\ 8g(x) = -4x+8 \\ \boxed{g(x) = -\dfrac{1}{2}x + 1}[/tex][tex]f \circ g = f\Big(g(x) \Big) = f\Big(-\dfrac{1}{2}x + 1\Big) = -\Big(-\dfrac{1}{2}x + 1\Big) + 2 = \\ \\ =\dfrac{1}{2}x-1+2 = \dfrac{1}{2}x + 1 \\ \\ g\circ f = g\Big(f(x)\Big) = g\Big(-x+2\Big) = -\dfrac{1}{2}\Big(-x+2\Big)+1 = \\ \\ = \dfrac{1}{2}x-1+1 = \dfrac{1}{2}x[/tex]
