A function \(f\) is such that \(f(x)=\ln(2x+1)\), for \(x\gt -\frac12\).

(a) Write down the range of \(f\).

A function \(g\) is such that \(g(x)=5x-7\), for \(x\in\mathbb R\).

(b) Find the exact solution of \(gf(x)=13\).

(c) Find the solution of \(f'(x)=g^{-1}(x)\).