Question

F(x)=sqrt x+2; g(x)=sqrt 8x-6. FInd f(g(x))

Answer 1

Hello!

This question is an example of composition of functions. It is using range values of some given function as domain values of some other given function to find new range values. Remember that the domain of the composite function will be the same as the domain of the first function.

Given f(g(x)), for f = $\sqrt{x+2}$, substitute x with g(x) = $\sqrt{8x-6}$.

Therefore, $f(g(x))= \sqrt{\sqrt{8x-6} +2}$.