[tex]If\ f(x)=y,\ then\ f^{-1}(y)=x.\\\\f(x)=4x-8\to4x-8=-2\qquad\text{add 8 to both sides}\\\\4x=6\qquad\text{divide both sides by 4}\\\\x=\dfrac{6}{4}\\\\x=\dfrac{3}{2}\\\\Answer:\ \boxed{f^{-1}(-2)=\dfrac{3}{2}}[/tex]
