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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?

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For example, finding the inverse graphically is not a formal justification. This may be what they are refering to.

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