Question

If f(x)=3x and g(x)=x-4, evaluate (fogon)(x)

Answer 1

\((f\circ g\circ n)(x)~?\) What's \(n\)?

Answer 2

i think that should say (f of g of)(x) so just f composite g

Answer 3

If it is just (fog)(x) ie f of g of x, or f composite g like zzrocker said, then you replace all x's in the f(x) function with the whole g(x) function. Ill get you started,
f(x)=3x
g(x)=x-4

(fog)(x)= 3 ( g(x) )

Answer 4

The answer is 3x^2-15 , I don't know how to get there. I've tried to combine 3x and x-4 as many ways as possible and I still can't get 3x^2-15.

Answer 5

do me a favor and confirm that you are giving us the question correctly, and make sure that the answer is for the right question. I believe that we are missing out on information from the question.

Answer 6

Let g(x)=x-4, h(x)-x^2-1, and f(x)=3x. Evaluate the following:

(fogon)(x)

Answer 7

is that n suppose to be an h, or vice versa?

Answer 8

The only thing that I can think of is that the n is supposed to be an h.

Answer 9

Yes, I think so

Answer 10

I caught is as I was typing it out.

Answer 11

It should be, I just worked it out and it came out to your answer. Try it yourself and let me know if you are having any more trouble with it.

Answer 12

I don't see how to get 3x^2-15. I got 3x^4-12x^3-3x^2+12x, which doesn't reduce to 3x^2-15

Answer 13

Here, this might help you get started:
f(x)=3x
g(x)=x-4
h(x)=x^2 -1

Start out with just goh(x) first:
goh(x)=(x^2-1)-4

then use that in fogoh(x):
fogoh(x)=3((x^2-1)-4)

Answer 14

note that (x^2-1)-4 is NOT distributive property

Answer 15

Ok, so you get 3(x^2-5) which comes out to the answer, but where did the x in x-4 go?

Answer 16

it also gets substituted in the equation, the x in x-4 became h(x), or x^2-1. so:
g(x)=x-4
goh(x)= (h(x))-4
notice that h(x) substitutes for x
goh(x)= (x^2-1)-4

same thing for f(x)

Answer 17

OK, I see it. For some reason I was trying to multiply it all out instead of substituting in place of the x's. Thanks for your help!

Answer 18

no problem =)