Does "inverting" distribute over addition? Is this equation always true, for any functions $f(x)$ and $g(x)$? $$(f(x)+g(x))^{-1} = f^{-1}(x) + g^{-1}(x)$$
By $^{-1}$ I mean inverse of the function, not $1$ divided by it.
edit... the answer is no. please see my other question instead Which functions make it true? $(f(x)+g(x))^{-1} = f^{-1}(x) + g^{-1}(x)$
No, it does not hold, take for example $f(x)=g(x)=x$.