Prove that the real image of the object is always inverted, and the imaginary one is always upright.

In all of the imaging examples, the actual image is obtained only in the diffusing lens and only if the object is behind the focal plane of the lens. And the image is always upside down.
If the object is between the collecting lens and the focus, then the image is imaginary and direct. A ghost and direct image is always obtained also in a diffusing lens.

Remember: The process of learning a person lasts a lifetime. The value of the same knowledge for different people may be different, it is determined by their individual characteristics and needs. Therefore, knowledge is always needed at any age and position.