Posted by Amy on Wednesday, December 21, 2011 at 12:05pm.
Having a bit of a problem with this
for the given functions f, g and h. find f*g*h and state the exact domain of f*g*h Please show all your work
f(x) = inx
g(x) = x 169
h(x) = 9x^2

pre calculus  Steve, Wednesday, December 21, 2011 at 2:14pm
I assume
by inx you mean ln x
f*g*h means multiplication.
domain of f is x>0
domain of g and h is all reals
so, domain of f*g*h i x>0
f*g*h = (ln x)(x  169)(9x^2)
= (9x^3  1521x^2)ln x
Now, if by f*g*h you mean f(g(h(x))) then
f(g(h)) = f(g(9x^2))
= f(9x^2  169)
= ln(9x^2  169)
Just looking at that, we see that 9x^2  169 must be > 0, so x > 13/3
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