The function \(f\) is defined by

\(f:x\mapsto(2x+3)^2,\qquad x\gt0.\)

(a) State the range of \(f\).

(b) Explain why \(f\) has an inverse.

(c) Find \(f^{-1}\).

(d) State the domain of \(f^{-1}\).

(e) Given that

\(g:x\mapsto\ln(x+4),\qquad x\gt0,\)

find the exact solution of \(fg(x)=49\).