# function composition problem

• Mar 22nd 2010, 06:09 PM
function composition problem
Let h be defined as $h(x) = \sqrt{\sqrt{(x-3-9)}}.$Express h as a composition $f \circ g$. Identify f and g and state the domain and range of each of h, f and g.

Thanks guys.
• Mar 22nd 2010, 07:20 PM
TKHunny
Are you sure about the argument under the radical? It seems a little odd.

Actually, x - 3 - 3 would make it more fun.

Anyway, try $f(x) = \sqrt{x}$ and $g(x) = x - 3 - 9$. This gives f(f(g(x))) = h(x). Or we could have r(x) = x - 3 and get f(f(g(g(g(g(x)))))). Okay, I'm having too much fun. (Giggle)
• Mar 23rd 2010, 10:33 PM
hey sorry bout the late reply..internet was down after moving house

its meant to be

$h(x) = \sqrt{\sqrt{(x-3}-9)}.$

cheers
• Mar 24th 2010, 12:34 AM
mr fantastic
Quote:

Originally Posted by smplease
hey sorry bout the late reply..internet was down after moving house

its meant to be

$h(x) = \sqrt{\sqrt{(x-3}-9)}.$

cheers

One obvious possibility is $f(x) = \sqrt{x}$ and $g(x) = \sqrt{x - 3} - 9$. I hope you see why.

There is another possibility, left for you to find.