[tex]g(h(x))=g(\sqrt{x+7})=\dfrac{2}{\sqrt{x+7}+9}\\\\f(g(h(x)))=f\left(\dfrac{2}{\sqrt{x+7}+9}\right)=7\cdot\left(\dfrac{2}{\sqrt{x+7}+9}\right)+9\\\\f(g(h(x)))=\dfrac{14+9\sqrt{x+7}+81}{\sqrt{x+7}+9}\\\\(f\circ g\circ h)(x)=\dfrac{95+9\sqrt{x+7}}{9+\sqrt{x+7}}[/tex]
With some extra effort, the radical can be removed from the denominator. That result is
[tex](f\circ g\circ h)(x)=\dfrac{9x+14\sqrt{x+7}-792}{x-74}[/tex]
The preferred form would be the one with the radical in the denominator, as it correctly shows the domain of the function to be x ≥ -7. The function actually is defined at x=74, which the "rationalized" form does not show.
