Curious Question about a concave mirror?

If I look into a concave mirror with a certain focal length (f) and then move closer so I'm less than the original focal length, wouldn't the image of myself be inverted? How about if I go greater than twice the focal length? Wouldn't that object be upright when I'm 2f away from it? And why between f and 2f I can't see an object, but it is formed? Weird?