# Math Help - Domain

1. ## Domain

Find the natural domain of the function gf.

f(x)= √x g(x)= x-5

Thanks.

2. 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 $x \geq 0$.

3. 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 $x\ge 5$.