Question

Domain and range of x^2+7x+12(its all under the square root)

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

i got -4 and -3

Answer 5

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

Answer 6

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

Answer 7

ok

Answer 8

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

Answer 9

no

Answer 10

then what is it?

Answer 11

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

Answer 12

\[(-\infty + 4)(-\infty+3) = ? \]

Answer 13

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).

Answer 14

thanks

Answer 15

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

Answer 16

range?

Answer 17

my brain is a bit fried from java programming last week

Answer 18

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

Answer 19

x?

Answer 20

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

Answer 21

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?

Answer 22

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

Answer 23

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.