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  1. explanation

    Step-by-step explanation:

    The square root of a negative number, such as StartRoot negative 144 EndRoot, is undefined. Explain why the square root of –x, StartRoot negative x EndRoot, is not necessarily undefined and what this means about the domain and range of f(x) = StartRoot negative x EndRoot.

  2. see the explanation

    Step-by-step explanation:

    we have

    [tex]f(x)=\sqrt{-x}[/tex]

    we know that

    The radicand of the function cannot be a negative number

    so

    [tex]-x\geq 0[/tex]

    Solve for x

    Multiply by -1 both sides

    [tex]x\leq 0[/tex]

    The domain of the function f(x) is the interval -----> (-∞, 0]

    The domain is all real numbers less than or equal to zero

    The range of the function f(x) is the interval ----> [0,∞)

    The range is all real numbers greater than or equal to zero

    Example

    For x=144

    [tex]144\leq 0[/tex] ----> is not true

    This value of x not satisfy the domain

    substitute

    [tex]f(x)=\sqrt{-144}[/tex] ----> this value is undefined

    For x=-144

    [tex]-144\leq 0[/tex] ----> is true

    This value of x satisfy the domain

    substitute

    [tex]f(x)=\sqrt{-(-144)}[/tex]

    [tex]f(x)=\sqrt{144}[/tex]----> this value is defined

    therefore

    The function will be undefined for all those values of x that do not belong to the interval of the domain of the function

  3. f(x) = √-x

    Step-by-step explanation:

    f(x) = √-x

    Step 1: Obtain the value of x (start)

    Step 2: The square root  of  -x

    Step 3: Write down the value of f(x) (End)

  4.   It has the same domain as the function [tex]f(x)=-\sqrt{-x}[/tex].

    Step-by-step explanation:

    The function ...

      [tex]f(x)=\sqrt{-x}[/tex]

    has a domain of all non-positive numbers and a range of all non-negative numbers. Anything with a -x under the radical will have the same domain. Any positive root will have the same range.

    __

    So, we can say it has the same domain as ...

      [tex]f(x)=-\sqrt{-x}[/tex]

  5. If x is a negative number, then negative x is a positive number and the square root can be determined. Therefore, the domain of the function is x ≤ 0. As a result, the range is never negative either, so it is y ≥0.

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