The function \(g\) is defined, for \(x\gt -\dfrac12\), by

\(g(x)=\frac{3}{2x+1}.\)

(i) Show that \(g'(x)\) is always negative.

(ii) Write down the range of \(g\).

The function \(h\) is defined, for all real \(x\), by \(h(x)=kx+3\), where \(k\) is a constant.

(iii) Find an expression for \(hg(x)\).

(iv) Given that \(hg(0)=5\), find the value of \(k\).

(v) State the domain of \(hg\).