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Math Help - help with functions

  1. #1
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    help with functions

    Find functions f and g such that h(x) = f(g(x)). Note: do not choose f(x) = x or g(x) = x

    22. h(x) = ln(x^3) 23. h(x) = (ln x)^3


    The answer to 23 is: f(x) =x^3
    g(x) = ln x

    but I dont understand how to get it. Sorry if this is incredibly simple, and thanks for any help
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  2. #2
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    Quote Originally Posted by Yamahammer342 View Post
    Find functions f and g such that h(x) = f(g(x)). Note: do not choose f(x) = x or g(x) = x

    22. h(x) = ln(x^3) 23. h(x) = (ln x)^3


    The answer to 23 is: f(x) =x^3
    g(x) = ln x

    but I dont understand how to get it. Sorry if this is incredibly simple, and thanks for any help
    Remember that the "x" in f(x)= some expression is a "place holder". f(x)= x^3, f(a)= a^3, f(b)= b^3. Whatever is in the parentheses on the left replaces the x in the formula. If g(x)= x^3, f(g(x))= f(x^3) and, with f(x)= ln(x), that becomes f(g(x))= f(x^3)= ln(x^3).

    f(g(x)) means "first do g(x), then apply f to that". "first do g(x)" gives g(x)= ln(x) and, since f(x)= x^3, "apply f to that" means to cube it: (ln(x))^3.

    Of course the answer to 22 is f(x)= ln x, g(x)= x^3 so that f(g(x))= f(x^3)= ln(x^3)
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