Composition of two functions: Advanced

Question

anonymous · Answer

attachment

anonymous · Answer

$$g(h(x)) = 2 (\sqrt{x+5})+5$$

anonymous · Answer

not sure how to approach my next step

anonymous · Answer

as far as I can tell, you can't reduce it any more than it already is. when the discriminant is addition like that, there isn't much more to do with it

anonymous · Answer

$$2(\sqrt{x}) + 2(\sqrt{5}) + 5$$?

anonymous · Answer

hm ok @DemolisionWolf i'll just leave it as it is

anonymous · Answer

noh, you can't do that with radicals

anonymous · Answer

domain is (-5,infinity)

anonymous · Answer

or is that a bracket? [-5, infinity)

anonymous · Answer

pretty sure it includes -5 so it should be a bracket

anonymous · Answer

sqrt( -5 + 5) = sqrt(0) = 0, so ya, include -5

anonymous · Answer

versus
sqrt( -6 + 5) = sqrt(-1) = no good

anonymous · Answer

thanks @DemolisionWolf

anonymous · Answer

sure thing

anonymous · Answer

have you ever heard of wolframalpha?

anonymous · Answer

yes i have i haven't used it though

anonymous · Answer

from what I can tell from how much you already know and get, there are just little things you have questions on, so using wolfram alpha might be faster than openstudy, if you are ever in a pinch.

anonymous · Answer

sweet i appreciate the recommendation!  ill look into it now :)