Let see if I can explain it in English, the most common meanings of "invertir" are: 1. When you change the order of something, 1+3 = 4 you could exchange the first numbers 3+1 = 4, this is "invertir" (inversión). 2. Save money and make some investments like buying in a stock market, that is "invertir" (to invest), then you have in your hand an investment (una inversión)

Inversa, normally we use it like " a la inversa" is an adverbial phrase, maybe in English is similar to "on the contrary".

Saludos.