Decomposing a function as a composition

Find f(x) and g(x) such that h(x)=(fog)(x)

h(x)=x^{2}-3x/square root of x+5

I tried to do it but I do not think is right. this is the answer I get: f(x)= x^{2}-3x g(x)= 1/square root of x+5

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- Oct 8th 2012, 04:36 PMmysisiCreate a decomposition of functions
Decomposing a function as a composition

Find f(x) and g(x) such that h(x)=(fog)(x)

h(x)=x^{2}-3x/square root of x+5

I tried to do it but I do not think is right. this is the answer I get: f(x)= x^{2}-3x g(x)= 1/square root of x+5 - Oct 8th 2012, 05:26 PMjohnsomeoneRe: Create a decomposition of functions
Your answer was a quotient, not a composition. You found f and g so that h(x) = f(x)/g(x).

There are an unlimited number of choices given the way the problem is stated.

For instance, there are always these trivial choices:

Choice #1) f(x) = h(x) and g(x) = x

Choice #2) f(x) = x and g(x) = h(x)

Maybe more interesting is letting g(x) = x+5.

Then and , so

, where

Choice #3)

Now try . Note that (actually, it can't be allowed to be 0). Have .

Thus and , so

Thus

(now use to know that )

, where

Choice #4) - Oct 9th 2012, 07:58 AMmysisiRe: Create a decomposition of functions
Hi! Thanks for answering my question. However my professor said that is not the way he wants it. He said that the answer g(x) should be g(x)=1/square root of x+5 and I only need to find f(x). I guess he only wants a quotient? Mine is wrong.Can you help me please?? So when I find (fog) I will end up with: x^2-3x/ square root of x+5 back again. Thanks!!

- Oct 9th 2012, 08:04 AMjohnsomeoneRe: Create a decomposition of functions
Review what I did for Choice #3 and Choice #4. In each case, I began with choice of g(x) (one time was x+5, the other it was sqrt(x+5)). Then I did some algebra and eventually found f(t) such that h(x) = f(g(x)). So if you repeat that process, you'll solve the problem. Repeat the process I did, only now your choice of g(x) will be:

.