Question

Find the inverse of h(x) = 3/-x-2

Answer 1

`h(x)=(3)/(-x-2)\to y=(3)/(-x-2)\\\\Domain:\ x\\eq-2\\\\\text{Interchange the y and the x}\\\\x=(3)/(-y-2)\\\\\text{Solve for y}\\\\x=(3)/(-y-2)\\\\(x)/(1)=(3)/(-y-2)\qquad|\text{cross multiply}\\\\x(-y-2)=3\qquad|:x\\eq0\\\\-y-2=(3)/(x)\qquad|+2\\\\-y=(3)/(x)+2\qquad|\text{change the signs}\\\\y=-(3)/(x)-2\\\\Answer:\ \boxed{h^(-1)(x)=-(3)/(x)-2}\ for\ x\\eq0`