how do you solve this composition functions problem? h(x)= 3x^2-2, g(x)=3x-3.

Question

chriss · Answer

Which composition are you looking for?  g o h would be g(h(x)) and you would plug the h(x) expression in for x on the g(x) expression.

$$g(h(x))=3(3x ^{2}-2)-3$$
$$=9x ^{2}-6-3$$
$$=9x ^{2}-9$$

anonymous · Answer

is this answer simplified?

chriss · Answer

well you could factor out the 9 to get
$$9(x ^{2}-1)$$

anonymous · Answer

how would you do it if you had to foil it?

chriss · Answer

also, you didn't specify which composition, so I just picked one... you could also do a composition for h o g

anonymous · Answer

h o g is the composition. sorry.

chriss · Answer

I'm not sure what you would want to foil...  although the h o g composition would require use of foil...

ah.. ok.. gimme a sec to work it out.

anonymous · Answer

ok thank you.

chriss · Answer

So you start out with h(3x-3).  Which means you are plugging the expression 3x-3 in for x in the expression 3x^2-2

$$h(g(x))=3(3x-3)^{2}-2$$
(foil the (3x-3)^2 first)
(3x-3)(3x-3)
$$=9x ^{2}-18x+9$$
(plug that back into the h(g(x)) expression
$$3(9x ^{2}-18x+9)-2$$
$$27x ^{2}-54x+27-2$$
$$27x ^{2}-54x+25$$

chriss · Answer

And I think that's as simplified as you can get it.

anonymous · Answer

Thank you. That's the answer i was looking for.

chriss · Answer

You're welcome