# Domain

• Oct 10th 2009, 12:26 AM
Oasis1993
Domain
Find the natural domain of the function gf.

f(x)= √x g(x)= x-5

Thanks.
• Oct 10th 2009, 01:05 AM
mr fantastic
Quote:

Originally Posted by Oasis1993
Find the natural domain of the function gf.

f(x)= √x g(x)= x-5

Thanks.

$g(f(x)) = f(x) - 5 = \sqrt{x} - 5$.

The implied domain is clearly $x \geq 0$.
• Oct 10th 2009, 06:07 AM
HallsofIvy
But I would have interpreted "gf" as the product, $(x- 5)\sqrt{x}$ which also has natural domain $x\ge 0$. The composition the other way, $f\circ g(x)= \sqrt{x- 5}$, on the other hand, has natural domain $x\ge 5$.