Are additive inverses the same as opposites?

The opposite is defined in the context of an operation.

So, if the operation is addition, then the opposite is the additive inverse. If the operation in multiplication, then the opposite is the reciprocal. If the operation is exponentiation then the opposite is the logarithm, if the operation is sine then the opposite is arc sine.

In function notation,

if y = f(x) then the opposite is x = f-1(y), which may or may not always be defined.