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pre calculus

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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 -

    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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