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Math Help - Find the domain and range

  1. #1
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    Find the domain and range

    g(x) = sqrt.(25 - x^2)
    r(x) = |2x - 3|

    plz help me thanks!
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  2. #2
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    Hello, NeedHelp18!

    Find the domain and range.

    1)\;\;g(x) \:= \:\sqrt{25 - x^2}

    We can see that (25-x^2) must not be negative.

    We have: . 25-x^2 \:\geq \:0

    Then we have: . -x^2 \:\geq \:-25

    Multiply by -1: . x^2 \:\leq \:25

    And we have: . |x| \:\leq \:5

    . . \boxed{\text{Domain: }\;-5 \:\leq\:x\:\leq\:5}


    We see that g(x) is never negative: . g(x) \:\geq\:0


    When x=0,\;g(0) \:=\:\sqrt{25} \:=\:5 (maximum value)

    . . \boxed{\text{Range: }\;0 \:\leq \:g(x) \:\leq \:5}




    2)\;\;r(x) \:= \:|2x - 3|

    We can use any value for x.

    . . \boxed{\text{Domain: }\:(-\infty,\:\infty)}


    An absolute value is never negative: . r(x) \:\geq\:0

    As x \to \pm\infty,\;r(x) \to \infty

    . . \boxed{\text{Range: }\;r(x) \:\geq 0}

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