Could you please name some examples of classical music where there are pieces in which certain intervals AND their inversions are profusely/prominently used (=play important role in the composition)?
This sounds a little like a homework question, so I'll abstract it slightly in the hopes of leading you in the right direction without fulling giving you the answer. (I'll also use a much lesser-known musical example.)
By "inverting" an interval, we mean it just moves in the other direction. Think of the famous opening to Beethoven 5: dun-dun-dun-DUNNNN, where the last note is a third lower than the others. If we invert this last interval, the last pitch will be a third higher than the others.
At this point in the opening of the Adagio to Bruckner 8, the violins come in. Hear how they eventually go up one pitch and then move back down to the original one? Then, right afterwards, they go down one pitch and back up.
This would be an example of using inverted intervals, but it's intentionally a very silly one. If this is for a homework question, consider this a friendly tip that your teacher will find it suspicious if you mention the Adagio of a Bruckner symphony :-)