# Been stuck on this 'f o g' maths question all week and can't resolve it!

• Mar 31st 2011, 03:57 AM
hellomoto89
Been stuck on this 'f o g' maths question all week and can't resolve it!
let h be defined by h(x) = root((1/x)+2). express h as a composition f o g. Identify f and g and state the domain and range of each of h, f and g.

I somehow got the wrong answer, if someone could give me a detailed explanation, that would be great!
• Mar 31st 2011, 04:01 AM
TheChaz
There are a couple correct answers. There is the cheesy one where you just let f(x) = root((1/x) + 2) .... (i.e. the whole thing) and let g(x) = x ... (the identity).
But most teachers would not appreciate the beauty of that answer.

You could also consider the "root" to be one function, and everything else to be the other. So g(x) is what's inside the root...
g(x) = 1/x + 2
f(x) = root(x)
or
g(x) = 1/x
f(x) = root(x + 2)
• Mar 31st 2011, 04:32 AM
DrSteve
The "best" answer is Chaz's first answer. The reason is that f and g there are both "elementary" functions. They themselves do not need to be decomposed before performing Calculus, for example.
• Mar 31st 2011, 04:50 AM
hellomoto89
Thanks Chaz, decided to go with g(x) = 1/x + 2 and f(x) = root(x)

but with the domain and range having problems

f(x) domain = x>>0 and range = y>>0
g(x) domain= -infinity->0 and 0->infinity range = im not too sure

also not too sure about h(x) range and domain