Composite Function question:
If f(x)=sqrt(x-4) and g(x)=3x^2-21 find indicated composite function. Show all work.
I've ended up with (gof) (x)=sqrt(3x^2-25) but my online assessment says this is incorrect?

Question

Composite Function question: 
If f(x)=sqrt(x-4) and g(x)=3x^2-21 find indicated composite function. Show all work. 
I've ended up with (gof) (x)=sqrt(3x^2-25) but my online assessment says this is incorrect?

kainui · Answer

Ahh, what you've done is the opposite, you found (fog) not (gof) so just do it the other way around. =)

anonymous · Answer

oh how would I be able to do that? I thought I did switched it, which is why I came up with this problem?

anonymous · Answer

work from the inside out 
$$g(f(x))=g(\sqrt{x-4})$$

anonymous · Answer

then since 
$$g(\spadesuit)=3\spadesuit^2-21$$ you get 
$$g(\sqrt{x-4})=3(\sqrt{x-4})^2-21$$ which you can probably simplify a bit

anonymous · Answer

Thanks to your advice, I've gotten $$3(\sqrt{x-17})^2$$ but the online assessment still consider this wrong?

anonymous · Answer

@satellite73

anonymous · Answer

oh no

anonymous · Answer

$$\sqrt{x-4}^2=x-4$$

anonymous · Answer

so you have 
$$3(x-4)-21$$ as a first step

anonymous · Answer

and then ending up with (3x-12)-21 the second step? Sorry I feel so slow asking all these questions @satellite73

anonymous · Answer

yes that is right

anonymous · Answer

then I would result in 3x-9 I believe? @satellite73