[tex]h(x)=\dfrac{3}{-x-2}\to y=\dfrac{3}{-x-2}\\\\Domain:\ x\neq-2\\\\\text{Interchange the y and the x}\\\\x=\dfrac{3}{-y-2}\\\\\text{Solve for y}\\\\x=\dfrac{3}{-y-2}\\\\\dfrac{x}{1}=\dfrac{3}{-y-2}\qquad|\text{cross multiply}\\\\x(-y-2)=3\qquad|:x\neq0\\\\-y-2=\dfrac{3}{x}\qquad|+2\\\\-y=\dfrac{3}{x}+2\qquad|\text{change the signs}\\\\y=-\dfrac{3}{x}-2\\\\Answer:\ \boxed{h^{-1}(x)=-\dfrac{3}{x}-2}\ for\ x\neq0[/tex]
