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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