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Isn't this a case of multiplication being such a "well-known" function that the "inverse" defaults to "multiplicative inverse"?

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No, inverse means reciprocal only when the context is a number or algebraic variable.

If we're talking about trig functions, inverse sine or arcsine is very different than just the reciprocal of the sine.

If we're talking about images, inverse usually means "rotate 180 degrees" or "color inversion".

I think we’re on the same page. The point I was trying to make is that reciprocal/multiplicative inverse in every day use seems like it’s a property of a number and not of a function only because most people just assume that the function we’re inverting is multiplication. The comment I was replying to missed that.

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