Question

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Answer 1

$f:\mathbb{R}\to \mathbb{R},\quad f(x) = x^2+3x+1 \\ \\ f \circ g = g\circ f \Rightarrow f\Big(g(x)\Big) = g\Big(f(x)\Big)\\ \\ \\ \text{Pentru }x = -1:\quad f(-1) = 1-3+1 = -1\Rightarrow f(-1) = -1\\ f\Big(g(-1)\Big) = g\Big(f(-1)\Big) \Leftrightarrow f\Big(g(-1)\Big) = g(-1)\\ \\ \text{Daca}: g(-1) = -1 \Rightarrow f(-1) = -1\quad (A) \\ \\ \Rightarrow \text{Pentru }a = -1,\quad g(a) = a$