How to make the following concave function to fit cvx?

[Mark_L_Stone]

Can CVX solve this kind of function {x-log(1+0.01*x/(x+1))}

Let aa = a/g; bb=b/g; log(1+aa*t/(bb+t)) = log(1+aa-aa*bb*inv_pos(bb+t)), the latter of which complies with CVX’s rules. So this generalizes (adapts) the reformulation provided above by @Michal_Adamaszek to bb not necessarily equal to 1.