Question

we need help with domain.

Answer 1

The domain of a function is the set of all possible input values yield an output for the function.

Answer 2

If you have other questions about that (or something related) feel free to clarify.

Answer 3

\[y=\sqrt[3]{x-6?}\over \sqrt{x ^{2}-x-30}\]

Answer 4

domain:Domain: The domain of a function is the set of all possible input values (usually x), which allows the function formula to work

Answer 5

Well, this is a fraction as well as a radical, so there are two things that we have to worry about, division by zero, and negatives under the square root

Answer 6

lets being by factoring whats inside the square root, what do you get when you factor that quadratic?

Answer 7

there is no cubed root of 6 Langrange

Answer 8

i am talking about the one in the denominator

Answer 9

(x-6)(x+5)

Answer 10

correct, this means that the they ploymial is zero and these values.

Answer 11

so what would the domain be considering that

Answer 12

Well you cannot have the denominator be 0 because dividing by 0 is not allowed.

Answer 13

Therefore what can x NOT be, to ensure that the denominator is NOT 0?

Answer 14

so polpak what would the domain be, we are rather confused

Answer 15

I just gave you a hint. What values of x will make the denominator be 0?

Answer 16

x can not be postive 6 or negative 5, sorry comp. froze

Answer 17

That is correct!

Answer 18

Additionally, we cannot have that the product of the two is negative

Answer 19

Because that would give a negative under the square root

Answer 20

So for which values of x will the product be positive?

Answer 21

positve for values, less than -5 and greater than 6

Answer 22

sorry the computer keeps locking and so would it be (-infinty to 5] U [6 to infinity)?

Answer 23

You cannot include -5 and 6 remember? otherwise you'd have 0 and you cannot allow that.

Answer 24

ok thanks! what about \[y=\log(2x-12)\]

Answer 25

The argument to this log function has to be positive

Answer 26

that goes for are log functions regardless of base

Answer 27

Since your argument is 2x - 12, then the domain is the set of x-values which make 2x - 12 positive. In other words:
2x - 12 > 0

Answer 28

The domain will be the solution to this inequality. Can you solve this inequality?

Answer 29

2x-12>0?

Answer 30

so anything greater than 6 b/c that is what x equals.

Answer 31

Right

Answer 32

Any x value greater than 6 is valid for that function.

Answer 33

correct

Answer 34

The domain, then, is all numbers greater than 6. In interval notation this would be: (6, infinity).

Answer 35

Denominators cannot be 0, logs cannot be 0 or negative, even roots (square, 4th, 6th, etc) cannot be negative.

These are the restrictions on domain.

Answer 36

Or at least the ones you'll be working with

Answer 37

Even negative exponents just result in positive fractions, not in negative numbers

Answer 38

would the answer just be 6 to infinity?

Answer 39

yes

Answer 40

the input of logs cannot be 0, so x cannot be 6

Answer 41

(6, infinity).

Answer 42

It's 6 to infinity, not including either end.

Answer 43

\[y=\sqrt{\tan x}\]

Answer 44

what about that

Answer 45

again, there is a square root, so we cannot have negatives under it. At what values does tanx produce a negative number

Answer 46

in other words, the domain is all values of x for which tan x is positive