Question

Express the following function, h(x) as a composition of two functions f and g.

h(x) = x^2/(x^2 + 4)

I've been trying to wrap my head around this, but can't seem to come to an answer. At first I wanted to say:

f(x) = x^2/x
g(x) = x^2 + 4

But then I realized that g(x) would have be put in both x values in f(x) which is not the function given. Any suggestions?

Answer 1

Try with

f(x) = x/(x+4)

what would g(x) be? :) :P

Answer 2

I assume to get a squared answer g(x) would equal x.

Answer 3

nope, composition of a function basically means you put one function inside of another

for example

if f(x) = x + 2
and g(x) = 2x + 2

then f(g(x)) = f(2x + 2) = (2x + 2) + 2 = 2x + 4

mhmm, do you understand or should I do a better example? :)

Answer 4

I understand. So then g(x) would equal x^2. So that x^2 would be inputted into the x values in f(x).

Answer 5

Correct :)

Answer 6

Awesome! Thanks a bunch, this question has been driving me crazy, haha.

Answer 7

Anytime!

I don't know how I saw the numbers. I was just thinking and it clicked. It all comes with practice, I suppose. xD

Answer 8

I suppose so. It would have been easier for me if it was like: (2x+1)^2 xD I would have figured that would out with no problem.

Answer 9

Anyways, welcome to OpenStudy :)

Answer 10

Thanks! OpenStudy has definitely been helpful for me so far :) Definitely helps if you are stuck.

Answer 11

You can also just cheat and go with

f(x) = x
g(x) = x^2/(x^2 + 4)

then f(g(x)) = x^2/(x^2 + 4)

but it's basically cheating, lol

Answer 12

LOL. I can imagine the teacher's reaction if you did something like that x'd

Answer 13

Oh my gosh, I can see what that's basically cheating, haha. Right? It's like waiitt a second XD

Answer 14

Or maybe they would think your really clever, who knows? However, I prefer not to find out xD

Answer 15

What would your reaction be, Agent, if you got an answer like that? x'd

Answer 16

I'd probably still accept it, I remember teaching this to a precalc class and thinking they still have to understand it, to do that.

Less cheaty other options are ones like

f(x) = (x-4)/x
g(x) = x^2 + 4

f(g(x)) = x^2/(x^2+4)

Answer 17

Nice. The possibilities are endless I'm sure. It'll just get more complicated xD

Answer 18

Actually the most cheaty option is

f(x) = x^2/(x^2+4)
g(x) = x

f(g(x)) = f(x) = lol

Answer 19

Put on your lollerskates for that last one.

Answer 20

g(x) = x^2/(x^2 + 4)
f(x) = x

g(f(x)) = g(x)

it just has to be a composition of the functions, they didn't specify whether it had to be f(g(x)) or g(f(x)) ;p

Answer 21

Or go for a ride on the lollercoaster

http://rianjs.net/images/lol/LOLLERCOASTER.gif

Answer 22

That gif. Is awesome xD

Answer 23

That's the first time I've seen that lollercoaster. LOL

Answer 24

The roflcopter is an old favourite http://www.kreativekorp.com/miscpages/omgwtfbbq/roflcopter.gif

Answer 25

Where do you find these stuff. ROFL. I've never seen this before. ROFLOL

Answer 26

Oh my gosh, haha! Brilliant.

Answer 27

Here's the lollerskates gif http://www.threadbombing.com/data/media/2/lollerskates.gif

lol i googled lollerskates

Answer 28

Steamloller http://bbsimg.ngfiles.com/1/5573000/ngbbs42bd6adc5beb9.gif

Answer 29

http://rofl.name/a/

x'd

Answer 30

x'd

Answer 31

hey, this applies to us because of the olympics going on xDD
http://rofl.name/media.php?q=aniascii_lolympics.gif

x'd

Answer 32

Thanks for opening me to awesome new world x'D But I have to go. Thanks so much for the help!

Answer 33

http://rofl.name/media.php?q=aniascii_kthxbye.gif

Cya! If you ever need any help, we'll be around. Just give us a tag like @agent0smith :)

Answer 34

Ah ok! I wasn't sure how to do that. Thank you :)

Answer 35

And, one last thing, my username is misleading. xD

Agent is smarter than me in lotsa stuff. xD

Answer 36

Your icon still cool though x'D I love cats so ya xD

Answer 37

I just recently put it up as my profile picture xD

Answer 38

@TheSmartOne your links don't work, i don't think you can link them individually?

The lolrus isn't happy about not being featured on that page http://bbsimg.ngfiles.com/1/5573000/ngbbs42bd67f355412.gif

Answer 39

Also @TheSmartOne I've got like 15 years on you, and a university degree of knowledge, too ;P

Answer 40

Just wait till I'm older than you ;)

Answer 41

Lol, cya guys!

Answer 42

See you around (:

Answer 43

You too! Bye~

Answer 44

doooodd x'd

Answer 45

LMFAO train http://bbsimg.ngfiles.com/1/5573000/ngbbs42bd73cb794b1.gif

Answer 46

If someone sets one of the functions as the identity function, they most likely completely understand this topic. But they might have been told to just do this every time and it will 'work' so I tell my students, after making the class guess what would be the easiest way, that they are not allowed to do it.

Answer 47

lmaoo x'd

Answer 48

http://livedoor.blogimg.jp/mankanshoku/imgs/2/4/24b38c3b.jpg

Answer 49

Let's all have a sip of lmaonade while we watch these. 3D roflcopter! http://orig02.deviantart.net/7044/f/2009/240/1/6/animated_roflcopter__by_rydian.gif Non-functioning tail rotor means it couldn't fly without spinning the body spinning, due to conservation of angular momentum.

Helicopters are interesting machines. A lot of smart people think they shouldn't be able to fly.