how do i evaluate this function ?

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  • 1 month ago
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    You are asked to find the domain of that function.

    The domain is a list of all possible inputs into the function that will result in a real output.

    Since your function is the fourth root, any negative value inside will result in a complex number so we know what's inside of it must be zero or positive.  We can now create an inequlality based on this info that we can solve:

    x² - 9x ≥ 0

    Factor an x:

    x(x - 9) ≥ 0

    We know if either of the two factors are zero then the product is zero which will satisfy the inequality.  Those roots are:

    x = 0 and 9

    We can then use those roots as pivots to find out which range(s) will count.

    if x > 9 we have positive times positive which is positive, in our solution set.

    if 0 < x < 9 we have positive times negative which is negative, not in our solution set.

    if x < 0 we have negative times negative which is postive, in our solution set.

    And again, the points 0 and 9 are valid solutions to our derived inequality so that solution is:

    x ≤ 0 and x ≥ 9

    since those values will result in a non-negative value under the fourth root, the result will be a real number.  This makes the above solution also the result of the domain for this function.

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