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for the given functions f and g find f o g and state the domain show all work f(x)=sqrt x-3 g(x)=x^2-7x+9

  • math -

    Usually f o g is defined as f(g(x))
    f o g = f(x^2 - 7x + 9)
    = √(x^2 - 7x + 9) - 3


    if you meant to type f(x) = √(x-3) make the necessary adjustments, I read it just the way you typed it, i.e.
    f(x) = √x - 3

  • math -

    Reiny,

    that is correct, but I cannot type the squareroot sign with my computer - how do I find the domain, of this function?

  • math -

    the only thing to worry about for the domain is that the expression
    x^2 - 7x + 9 > 0

    look at the corresponding parabola
    y = x^2 - 7x + 9
    it has x-intercepts of
    x = (7 ± √13)/2
    so it will be negative between those two values

    domain:
    x < (7 - √13)/2 OR x > (7+√13)/2

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