Question

find G o F, for f(x)=9x+6 and g(x)=4x^2 +9-1

Answer 1

first off, is this the same as g(f(x))?

Answer 2

I think it's not but I haven't found my notes on it yet....

Answer 3

Yes, the open circle let's you know that you have a "composition" of functions
I prefer the latter notation. g(f(x)), g composed of f of x

Answer 4

Understand how to attack this one if you're doing g(f(x))? Or still need some assistance? :D

Answer 5

I think I still need some help. hold on, I'll copy what ive got on paper

Answer 6

first let me correct my g(x) up there, it should be 9x-1 not 9-1.
I'm thinking it's something like 4(9x+6)^2 +9(9x+6) but I feel like those 9x's should be something else?

Answer 7

oh, and a -1 after that last (9x+6). sorry, been a long day haha

Answer 8

\[\huge g(x)=4x^2+9x-1\]
\[\huge g(f(x))=4f(x)^2+9f(x)-1\]
\[\huge g(9x+6)=4(9x+6)^2+9(9x+6)-1\]Yah it looks like you've got the right idea! :)

Answer 9

From here, you might want to expand everything out and simplify alil bit :D

Answer 10

ok, well after that I got (36x+24)^2 +81x+54-1 and thats where I'm kinda stuck

Answer 11

I have 4 possible answers, two of which contain 36x^2 +81x(and one with -81x) the other two answers are higher, like 324x^2

Answer 12

which in the case of multiple choice means I'm either on the right track, or about to fall for a trap haha

Answer 13

Woops, when you bring the 4 INSIDE the square, you have to be careful.
You can't simply bring it in, unless you apply the opposite operation of that square to it. You COULD bring in a 2, since 2^2 = 4.

Answer 14

First step is to expand the square, let's do it WITHOUT bringing in the 4. That should make things easier.\[\large g(9x+6)=4(81x^2+108x+36)+81x+54-1\]

Answer 15

Oh! ok, hang on

Answer 16

sorry, where'd you get the 108x?

Answer 17

\[\large (9x+6)^2=(9x+6)(9x+6)=(81x^2+54x+54x+36)\]

Answer 18

dang it... I always forget that

Answer 19

Then multiply each of those terms by 4 after you've done that.
Then you'll have a bunch of bananas, and you gotta combine some things.

Answer 20

bunch of bananas indeed. I got 324x^2+513x+197 which is one of my choices. awesome. thanks a ton!

Answer 21

Yay team \:D/