## anonymous 5 years ago Domain and range of x^2+7x+12(its all under the square root)

1. anonymous

$f(x)=\sqrt{x^2 + 7x + 12} \rightarrow \text{f(x) is defined }\forall x\text{ | }x^2 + 7x + 12 > 0$

2. anonymous

am new to this,that is how i meant it :)

3. anonymous

Right, so the function is defined so long as the stuff under the radical is greater than or equal to 0. So solve the quadratic and see where it equals 0 and where it's above/below. That will tell you what x values are ok.

4. anonymous

i got -4 and -3

5. anonymous

Sounds right.. so (x+4)(x+3) So when will this be negative?

6. anonymous

Remember that a product is negative only when it has an odd number of negative factors.

7. anonymous

ok

8. anonymous

so my domain is -4>= x >= -3 ?

9. anonymous

no

10. anonymous

then what is it?

11. anonymous

When x is very large and negative what will that product be?

12. anonymous

$(-\infty + 4)(-\infty+3) = ?$

13. anonymous

If you put in a value (any value in between -3 and -4, let's say -3.5 the result will be an imaginary number. The ABSOLUTE VALUE of X must be greater than -3 OR greater than -4. That means any number in between -3 or -4 must be excluded! (-inf, -3] U [-4, +inf).

14. anonymous

thanks

15. anonymous

The domain is (-inf, -3] U [-4, +inf).

16. anonymous

range?

17. anonymous

my brain is a bit fried from java programming last week

18. anonymous

God, I don't know what is wrong with me today. The range is (-inf, -3] U [-4, +inf). The domain is X.

19. anonymous

x?

20. anonymous

If you have a function y=f(x), x is the domain and y is the range.

21. anonymous

Imagine two sets. set D={A,B,C} and set R={3,5,7}. If some function "f" associates the letter A with the number 3, then f(A) =3 and A is in the Domain of f and 3 is in the range of f. Did that make any sense to you?

22. anonymous

ok cool, am good in math , not really in domain and range but thanks

23. anonymous

I understand totally. It took me a long, long time to understand the concept of domain and range. If you have the time find " Schaum's Outline Series: Theory and Problems of Set Theory and Related Topics" by Seymour Lipschutz and read page 45. It will explain everything you never wanted to know about Range and Domain and didn't know who to ask. LOL.