\( 19 \mathrm{~g} \) is the function with domain \( x \geqslant-3 \) such that \( \mathrm{g}(x)=x^{2}+6 x \)
(a) Write down the range of \( \mathrm{g}^{-1} \)
(b) Express the inverse function \( \mathrm{g}^{-1} \) in the form \( \mathrm{g}^{-1}: x \mapsto \ldots \)
