[tex](g\circ f)(x) = 4x+1 \\ f(x) = -3x+2 \\ \\ (g\circ f)(x) = 4x+1 \\ g\Big(f(x)\Big) = 4x+1 \\ g(-3x+2) = 4x+1 \\ -3x+2 = t \Rightarrow -3x = t-2 \Rightarrow 3x = -t +2 \Rightarrow x = -\dfrac{1}{3} t +\dfrac{2}{3} \\ \\ \Rightarrow g(t) = 4\cdot \Big(-\dfrac{1}{3}t + \dfrac{2}{3}\Big) +1 \Rightarrow g(t) = -\dfrac{4}{3} t + \dfrac{11}{3} \\ \\ \Rightarrow \boxed{g(x) = -\dfrac{4}{3} x + \dfrac{11}{3}}[/tex]
