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anonymous

  • one year ago

find the domain of the function. f(x) = sqrt 6-x

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  1. mathstudent55
    • one year ago
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    Is it \(\large f(x) = \sqrt{6 - x} \) ?

  2. anonymous
    • one year ago
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    A. (-∞, 6) (6, ∞) B. (-∞, sqrt6) (sqrt6 , ∞) C. (-∞, sqrt6] D. (-∞, 6]

  3. anonymous
    • one year ago
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    yes that is right student

  4. mathstudent55
    • one year ago
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    Look in the function. You have x inside a square root. What numbers can you not take the square root of?

  5. anonymous
    • one year ago
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    x

  6. mathstudent55
    • one year ago
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    No. Look at the examples below. Can you take all 3 square roots below? |dw:1439842157310:dw|

  7. anonymous
    • one year ago
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    no

  8. mathstudent55
    • one year ago
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    Can you take any of the square roots in the figure?

  9. anonymous
    • one year ago
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    no

  10. mathstudent55
    • one year ago
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    This is what my calculator does with those square roots. |dw:1439842248218:dw|

  11. mathstudent55
    • one year ago
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    You can take the square root of a positive number and of zero. You can't take the square root of a negative number.

  12. mathstudent55
    • one year ago
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    Now let's go back to your function. \(\large f(x) = \sqrt {6 - x} \) If x is a number that makes the inside of the square root negative, then that value of x cannot be allowed. We need the inside of the square root to be zero or positive. To find out which values of x gives us a zero or positive inside of the root, we must solve this inequality: \(\large 6 - x \ge 0\)

  13. anonymous
    • one year ago
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    ok makes since

  14. mathstudent55
    • one year ago
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    \(\large 6 - x \ge 0\) Subtract 6 from both sides: \(\large - x \ge -6\) Since we have -x, but we want just x, we multiply both sides by -1. When we multiply (or divide) both sides of an inequality by a negative number, we must change the direction of the inequality sign. \(\large -1(- x) \le -1(-6)\) \(\large x \le 6\)

  15. mathstudent55
    • one year ago
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    Now we know that the domain is all numbers less than or equal to 6. Now you can choose the correct interval from the choices. Do you understand interval notation and what the choices mean?

  16. anonymous
    • one year ago
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    nop and depends on what choices are you talking about my answers i have to choose from

  17. mathstudent55
    • one year ago
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    I mean the choices you were given as answers to this problem. You need to choose the one that means the same as \(\large x \le 6\) from A. (-∞, 6) (6, ∞) B. (-∞, sqrt6) (sqrt6 , ∞) C. (-∞, sqrt6] D. (-∞, 6]

  18. anonymous
    • one year ago
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    i choose you pickachu im joking is it d

  19. mathstudent55
    • one year ago
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    Correct. Great!

  20. anonymous
    • one year ago
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    thnx for your help miss or mister

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