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Math Help - find (f + g) (x) and its domain

  1. #1
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    find (f + g) (x) and its domain

    f(x) = 1 / squarroot(x)
    g(x) = x^2 - 4x

    how do i begin?
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  2. #2
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    (f+g)(x) = \frac{1}{\sqrt{x}} + x^2 + 4x

    What values can't you plug into the function?
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  3. #3
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    or anything negative?
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  4. #4
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    So your domain: x > 0 .. i.e. non-zero and non-negative values.
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  5. #5
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    Wow, so then (f/g)(x) would have the same domain?

    And so would (fog)(x)
    And so would (f + g)(x)

    for these same values of g and f???
    f(x) = 1 / squarroot(x)
    g(x) = x^2 - 4x
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  6. #6
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    (\tfrac{f}{g})(x) = \frac{\frac{1}{\sqrt{x}}}{x^2 - 4x} = \frac{1}{\sqrt{x} \left(x^2 - 4x\right)} = \frac{1}{x\sqrt{x}(x-4)}

    There's an extra restriction here. Remember, can't have a division by 0.

    (f \circ g)(x) = f(g(x)) = f(x^2 + 4x) = \frac{1}{\sqrt{x^2 + 4x}}

    Just like earlier analysis, we can't have a division by 0 nor a square root of a negative number. So, our domain is restricted to values such that: x^2 + 4x > 0
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