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 x3 g(x)=x^27x+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) = √(x3) 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 xintercepts 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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