anonymous
  • anonymous
find the domain of the function. f(x) = sqrt 6-x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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mathstudent55
  • mathstudent55
Is it \(\large f(x) = \sqrt{6 - x} \) ?
anonymous
  • anonymous
A. (-∞, 6) (6, ∞) B. (-∞, sqrt6) (sqrt6 , ∞) C. (-∞, sqrt6] D. (-∞, 6]
anonymous
  • anonymous
yes that is right student

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mathstudent55
  • mathstudent55
Look in the function. You have x inside a square root. What numbers can you not take the square root of?
anonymous
  • anonymous
x
mathstudent55
  • mathstudent55
No. Look at the examples below. Can you take all 3 square roots below? |dw:1439842157310:dw|
anonymous
  • anonymous
no
mathstudent55
  • mathstudent55
Can you take any of the square roots in the figure?
anonymous
  • anonymous
no
mathstudent55
  • mathstudent55
This is what my calculator does with those square roots. |dw:1439842248218:dw|
mathstudent55
  • mathstudent55
You can take the square root of a positive number and of zero. You can't take the square root of a negative number.
mathstudent55
  • mathstudent55
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: \(\large 6 - x \ge 0\)
anonymous
  • anonymous
ok makes since
mathstudent55
  • mathstudent55
\(\large 6 - x \ge 0\) 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. \(\large -1(- x) \le -1(-6)\) \(\large x \le 6\)
mathstudent55
  • mathstudent55
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?
anonymous
  • anonymous
nop and depends on what choices are you talking about my answers i have to choose from
mathstudent55
  • mathstudent55
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]
anonymous
  • anonymous
i choose you pickachu im joking is it d
mathstudent55
  • mathstudent55
Correct. Great!
anonymous
  • anonymous
thnx for your help miss or mister

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