\(m(x)=2x^2-6\to y=2x^2-6\ \ \ \ |add\ 6\ to\ both\ sides\\\\2x^2=y+6\ \ \ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=\dfrac{y+6}{2}\ \ \ \ |sqare\ root\ both\ sides\\\\x=\sqrt{\dfrac{y+6}{2}}\\\\Answer:\boxed{m^{-1}(x)=\sqrt{\frac{x+6}{2}}\ for\ x\geq-6}\)
