The function \(f(x)\) is invertible, but the function \(g(x)=k*f(x)\) is not invertible. Find the sum of all possible values of k.

\(\text{if }k \neq 0 \text{ then}\\ g^{-1}(x) = \dfrac 1 k f^{-1}(x)\\ \text{so the only value of }k \text{ for which }g(x) \text{ is not invertible is }k=0\\ \text{the sum of }0 \text{ is }0\)