Question

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

Answer 1

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

Answer 2

Reiny,

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

Answer 3

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