# Thread: Decomposing a function as a composition

1. ## Decomposing a function as a composition

Decomposing a function as a composition
Find f(x) and g(x) such that h(x)=(fog)(x)

h(x)= x2-3x/ square root of x+5

I know the correct answer for g(x) is = 1/square root of x+5. But I do not know what is f(x)?? Is the correct answer x2-3x??

2. ## Re: Decomposing a function as a composition

Originally Posted by mysisi
h(x)= x2-3x/ square root of x+5
Please write the function correctly or confirm that it is written correctly. You can write $\sqrt{z}$ as sqrt(z); however, this is not the biggest problem with the expression above.

There are many ways to represent a given function h(x) as a composition of f and g. For example, f(x) = h(x) and g(x) = x or f(x) = x and g(x) = h(x). So, "g(x) is = 1/square root of x+5" cannot be the correct answer unless the question provides more information.

3. ## Re: Decomposing a function as a composition

Two days ago you posted the exact same question: Create a decomposition of functions

You're not supposed to do this. It can create duplicate answers when, posted new, someone invests the time to help but merely repeats the help that someone else has already provided. That's being inconsiderate to those who are attempting to help you.

4. ## Re: Decomposing a function as a composition

Those are the only the instructions I got. This is another example from textbook:
If h(x)= 1/(x+3)^2 find f(x) and g(x) such that h(x) fog (x).
Solution: f(x) 1/x and g(x) (x+3)^3
(Copy it from textbook)
Sorry i am new to this forum

5. ## Re: Decomposing a function as a composition

Sorry but I am not being inconsiderate just trying to find the right answer.according to my professor your answer was not correct.

6. ## Re: Decomposing a function as a composition

Originally Posted by mysisi
Those are the only the instructions I got.
Really? In the thread from post #3 you wrote:
Originally Posted by mysisi
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
How is rejecting one legal answer f(x) = x, g(x) = h(x) and instead stipulating the g(x) must be $\frac{1}{\sqrt{x+5}}$ not additional instructions, which should be a part of the problem statement?

Here is what you should do, in my opinion. (1) Understand why there are many answers to the original question when g(x) and f(x) are not given. (2) Understand why the way you wrote h(x) and g(x) is incorrect (because of the order of operations). (3) Read carefully John's explanation in the previous thread. (4) Continue the previous thread by posting meaningful questions or solution attempts.