Can the inverse of a graph be a funtion even if the graph itself is not a function

Yes, if you mean if the original graph itself is not a function.consider the relation  . this is a sideways parabola that is not a function. it fails the vertical line test; there can be multiple outputs that map from a single input.but the inverse of it is a function. the inverse relation to  is  , which is a reflection of the former in the line  .in the attached photo,  blue:   (sideways parabola)black: (the line of reflection for inverse relations)red: (the inverse relation of blue)