Is it a concave function of $f(x)$ where $f(x)$ is an increasing function?

Question

I have a function $f(x)$ whose first derivative and second derivative are always positive. I want to know whether the following function will be concave or not $$g(x)=log(1+f(x))$$ $x$ can only take positive values and $f(x)$ is also positive always. Further, the double derivative of $f(x)$ is always positive (which means $f(x)$ is a convex function). Thanks in advance.