# Clarification - How would one find the inverse of a function “formally”?

I was doing my math homework about inverse functions, and I came across a problem that said "Find the inverse function of f informally.", where $$f(x) = \frac{1}{3}x$$. I know how to find the inverse function of a function like $$f$$, but my question is why did they question have to specify "informally"? Is there a formal way to find inverse functions? Or is it just a meaningless word?