Posted by **Sara** on Wednesday, January 11, 2012 at 9:04am.

for the given functions f and g find f o g and state the domain show all work f(x)=sqrt x-3 g(x)=x^2-7x+9

- math -
**Reiny**, Wednesday, January 11, 2012 at 9:09am
Usually f o g is defined as f(g(x))

f o g = f(x^2 - 7x + 9)

= √(x^2 - 7x + 9) - 3

if you meant to type f(x) = √(x-3) make the necessary adjustments, I read it just the way you typed it, i.e.

f(x) = √x - 3

- math -
**Sara**, Wednesday, January 11, 2012 at 9:28am
Reiny,

that is correct, but I cannot type the squareroot sign with my computer - how do I find the domain, of this function?

- math -
**Reiny**, Wednesday, January 11, 2012 at 9:42am
the only thing to worry about for the domain is that the expression

x^2 - 7x + 9 > 0

look at the corresponding parabola

y = x^2 - 7x + 9

it has x-intercepts of

x = (7 ± √13)/2

so it will be negative between those two values

domain:

x < (7 - √13)/2 OR x > (7+√13)/2

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