## anonymous one year ago find the domain of the function. f(x) = sqrt 6-x

1. mathstudent55

Is it $$\large f(x) = \sqrt{6 - x}$$ ?

2. anonymous

A. (-∞, 6) (6, ∞) B. (-∞, sqrt6) (sqrt6 , ∞) C. (-∞, sqrt6] D. (-∞, 6]

3. anonymous

yes that is right student

4. mathstudent55

Look in the function. You have x inside a square root. What numbers can you not take the square root of?

5. anonymous

x

6. mathstudent55

No. Look at the examples below. Can you take all 3 square roots below? |dw:1439842157310:dw|

7. anonymous

no

8. mathstudent55

Can you take any of the square roots in the figure?

9. anonymous

no

10. mathstudent55

This is what my calculator does with those square roots. |dw:1439842248218:dw|

11. 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.

12. 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: $$\large 6 - x \ge 0$$

13. anonymous

ok makes since

14. 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. $$\large -1(- x) \le -1(-6)$$ $$\large x \le 6$$

15. 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?

16. anonymous

nop and depends on what choices are you talking about my answers i have to choose from

17. 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]

18. anonymous

i choose you pickachu im joking is it d

19. mathstudent55

Correct. Great!

20. anonymous

thnx for your help miss or mister