Question

How to find the inverse of f(x) = -(3/-x-3) - 2

Answer 1

so, to get the inverse relation of anything, as you'd already know, we first do a quick switcharoo on the variables, and then solve for "y".


`\bf \stackrel{f(x)}{y}=-\cfrac{3}{-x-3}-2\qquad inverse\implies \boxed{x}=-\cfrac{3}{-\boxed{y}-3}-2 \\\\\\ x+2=\cfrac{3}{-(-y-3)}\implies x+2=\cfrac{3}{y+3}\implies (x+2)(y+3)=3 \\\\\\ xy+3x+2y+6=3\implies xy+2y=3-3x-6 \\\\\\ y(x+2)=-3x-3\implies y=\cfrac{-3x-3}{x+2}\implies \stackrel{f^(-1)(x)}{y}=\cfrac{-3(x+1)}{x+2}`