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Math Help - A few pre calc questions! help appreciated

  1. #1
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    A few pre calc questions! help appreciated

    f(x) = 3x^2-5 and g(x) = 2/x. find the function of f(g(x)) and give the domain.

    Solve equation with exact answers: -x^2-3x+10 = 0

    f(x) = ln(4-x) find the domain

    Help appreciated
    Thanks!
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  2. #2
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    Quote Originally Posted by Murphie View Post
    f(x) = 3x^2-5 and g(x) = 2/x. find the function of f(g(x)) and give the domain.

    Solve equation with exact answers: -x^2-3x+10 = 0

    f(x) = ln(4-x) find the domain

    Help appreciated
    Thanks!
    1) Substitute the x in f by the term of g:

    f(x)=3\cdot \left(\dfrac2x\right)^2-5 = \dfrac{12}{x^2}-5

    Since the division by zero is not allowed the domain is D=\mathbb{R}\setminus \{0\}

    2) -x^2-3x+10 = 0

    Use the quadratic formula to solve this equation. I've got x = -5~\vee~x = 2

    3) You are supposed to know that the ln-function is defined for positive arguments only. Thus the domain is D = \{ x | 4-x > 0\}_{ \mathbb{R}}
    Last edited by mr fantastic; December 14th 2008 at 01:01 AM. Reason: Removed reference to Jhevon's reply about not double posting
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