[tex]\bullet \ f(x) = 2x - 3 \\ \bullet f(g(x)) = -4x + 1 \\\\ \text{Se} \ g(x) = ax + b \\ f(g(x)) = 2 \cdot (ax + b) - 3 \\ f(g(x)) = 2ax + 2b - 3 \\\\ \text{Sabemos agora que:} \\ \bullet f(g(x)) = -4x + 1 \\ \bullet f(g(x)) = 2ax + 2b - 3 \\\\ \text{Ent}\tilde{a}\text{o:} \\ \bullet -4x + 1 = 2ax + 2b - 3 \\\\ \text{Em cada func}\tilde{a}\text{o desta igualdade, temos, respectivamente:} \\ \bullet \ a_1 = -4 \ e \ a_2 = 2a \\ \bullet \ b_1 = 1 \ e \ b_2 = 2b - 3[/tex]
[tex]\text{Sendo ambas iguais, temos:} \\ \bullet \ a_1 = a_2 \\ 2a = -4 \\ a = -2 \\\\ \bullet \ b_1 = b_2 \\ 1 = 2b - 3 \\ 2b = 4 \\ b = 2 [/tex]
[tex]\text{Se:} \\ \bullet \ a = -2 \\ \bullet \ b = 2 \\ \bullet \ g(x) = ax + b -2x \\\\ \text{Ent}\tilde{a}\text{o:} \\ \bullet \ g(x) = -2x + 2 \\ \bullet \ g(-1) = -2 \cdot (-1) + 2 \\ g(-1) = 2 + 2 \\\\ \boxed{g(-1) = 4}[/tex]
