Convergence of fixed point iteration when $g'(x^{*})= -1$.

Question

Consider the fixed point iteration given by $x_{n+1}=g(x_{n})$ where $g(x) = x - 2 + 4 e^{-x}$, and the fixed point of $g(x)$ is $\ln2$. Please show that whether or not this fixed point iteration will converge to the fixed point $\ln2$ if the initial point $x_{0} \neq \ln2$

Thanks.