Question

Can you solve this for me

Answer 1

`g(h(x))=g(√(x+7))=(2)/(√(x+7)+9)\\\\f(g(h(x)))=f\left((2)/(√(x+7)+9)\right)=7\cdot\left((2)/(√(x+7)+9)\right)+9\\\\f(g(h(x)))=(14+9√(x+7)+81)/(√(x+7)+9)\\\\(f\circ g\circ h)(x)=(95+9√(x+7))/(9+√(x+7))`

With some extra effort, the radical can be removed from the denominator. That result is


`(f\circ g\circ h)(x)=(9x+14√(x+7)-792)/(x-74)`

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.