Having a bit of a problem with this

Question

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

Answer 1

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