[tex]g(x)=-\dfrac{4}{3}x+2\to y=-\dfrac{4}{3}x+2\\\\\text{exchange x and y}\\\\x=-\dfrac{4}{3}y+2\\\\\text{solve for y}\\\\-\dfrac{4}{3}y+2=x\qquad\text{subtract 2 from both sides}\\\\-\dfrac{4}{3}y=x-2\qquad\text{multiply both sides by (-3)}\\\\4y=-3x+6\qquad\text{divide both sides by 4}\\\\y=-\dfrac{3}{4}x+\dfrac{6}{4}\\\\Answer:\ \boxed{g^{-1}(x)=-\dfrac{3}{4}+\dfrac{3}{2}}[/tex]
