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Math Help - [SOLVED] Domain and range confusion

  1. #1
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    [SOLVED] Domain and range confusion

    Okay so I have the function f(x) = square root of 9-x^2 and g(x) = square root x+3

    I must find f of g

    This is square root 9 - (square root x+3)^2

    Now I must find the domain and range. Here is my attempt:

    Simplified I have square root 6-x. Since x cannot be 6 or greater the domain must be (-infinity, 6). The range is (6, +infinity).
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  2. #2
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    Hello, thekrown!

    Given: . \begin{array}{cccc} (1) & f(x) &=& \sqrt{9-x^2} \\<br />
(2) & g(x) &=& \sqrt{x+3} \end{array}

    Find f\circ g

    f\circ g \;=\;\sqrt{9-(\sqrt{x+3})^2} \;=\;\sqrt{9-x-3} \;=\;\sqrt{6-x}


    The domain of f(x) is: . -3 \,\leq x \,\leq\,3

    The domain of g(x) is: . x \,\geq\,-3

    . . Hence, the domain of f \circ g is: . [-3 ,\;3]


    Hence, f\circ g ranges between: . \sqrt{6-(\text{-}3)}\,\text{ and }\,\sqrt{6-3}

    . . Therefore, the range of f\circ g is: . \left[ \sqrt{3},\:3\right]

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  3. #3
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    Got it!

    Okay, now the second half of this question is to find g of f

    Would the domain of this g of f be the same as f of g?
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