# Composite function proplem

• Sep 14th 2009, 03:13 PM
kevintrung
Composite function proplem
Determine if the FoG is defined, if it is not find the resriction of Go so that FoG is defined.

- f and g have domain of 0 to infinity
f(x)= root x
g(x)=3-2x

Edit: well my main problem is that i dont know how to find out if the 2 compostie functions is defined or not, pls explain that part for me thanks
• Sep 14th 2009, 03:26 PM
happyjohn38
$\displaystyle f=\sqrt{x}$ so f isn't definied for negative numbers, but luckily the domain is the non-negative numbers

g is defined for all real numbers, so we're good there

so $\displaystyle f(g)=\sqrt{3-2x}$ but we need 3-2x to be non negative, so you must restrict the domain of g to ensure that 3-2x only spits out non negative numbers
• Sep 14th 2009, 03:29 PM
kevintrung
so is there like general rule so that we can know if the 2 functions are defined ?
so the restriction of domain g would be from 3/2 to infinity ?

i got that answer but on the back of the book it says 0 to 3 is the restriction domain for g'
• Sep 14th 2009, 05:08 PM
kevintrung
some1 help ?