Question

how do you figure out the domain of an equation??
ex. (x^5 - 2)^7 .. what is the domain? .. but i want to know how to solve on my own

Answer 1

domain is the values x can be.

so, for instance, if you have an equation like y = x, x could be any number, there is nothing restricting it's value

Answer 2

if you have an equation like y = 1/x, x cannot be zero because you cannot divide by zero (it is undefined, doesn't make sense to split things up into 'zero' parts)

Answer 3

So, in essence, the domain is all of the possible values you can put into an equation.

On the flip side, the range is all the values that can come out. (irrelevant but good to know)

Answer 4

ok .. so any equation with a fraction that has a zero under is undefined? right

Answer 5

Well, it is undefined when x = 0. But it is defined for all other numbers other than 0.

Answer 6

aka the domain is every real number except 0

Answer 7

there are also several different ways to write the domain

one way to state the domain of f(x) = 1/x is

-infinity < 0 < infinity

meaning x can be equal to any number besides 0

Answer 8

ok
so the equation i showed.. since its all real numbers .. does that mean the answer would be \[(\infty, -\infty)\]

Answer 9

well, thats not really a good way to write it, but i think you get the idea

Answer 10

how would i write it?

Answer 11

the usual way to write it would be (-inf,inf)

Answer 12

oh ok

Answer 13

yeh.. i think im getting the hang of this... thank you so much!!!!

Answer 14

but its good to learn the domain of all basic functions

all polynomials have (-inf,inf) as a domain. the equation you listed is a polynomial, thus, it has that domain.

Answer 15

oh ok... im sorry but please explain further.. or give an example

Answer 16

http://www.analyzemath.com/DomainRange/domain_range_functions.html

Answer 17

look there at the first table. it will give you the domain of all basic functions

Answer 18

the first 5 cases listed are all polynomial equations

Answer 19

the first being a linear equation, 2nd quadratic, 3rd cubic, and then the general case x^n

Answer 20

ok

Answer 21

basically x raised to any number will always have (-inf,inf) has its domain

Answer 22

x^2

(x-2)^2

4x + 3x^2 - (x+4)^2 + x^5

all of these are polynomial equations, all have (-inf,inf) for a domain

Answer 23

if you understand the domain/range of the functions you have to use (there are only 8-10 ones you really need to know) it makes algebra a whole lot easier

Answer 24

i see that it says x^2 has -inf,inf and range is 0,inf and then it says f(x)=square root x domain and range is 0,inf
why?
arent they the same?

Answer 25

that is a special case where the power you are raising to is less than 0

you must understand that exponentiation is repeated multiplication

like, 2^4 just means 2*2*2*2 (2 multiplied by itself 4 times)

Answer 26

so what does it mean when you have something like 2^(1/2)?

you are multiplying 2 by itself... 1/2 times?

Answer 27

or in other words, what number multiplied by itself will give you 2?

Answer 28

the point of what i'm saying, is the domain of something like x^1/2 is

[0,inf)

Answer 29

the reason is because what you are doing is finding a number such that when you multiply it by itself it equals x

Answer 30

now the problem is, when you multiply a number by itself, it can never be negative

Answer 31

that is, a*a will always be a^2 and -a*-a will always be a^2

Answer 32

thus, a^2 can never be negative

Answer 33

thus, the domain of something like x^1/2 can never be negative

Answer 34

i hope that makes sense, it's kind've complicated with words lol

Answer 35

sorry.. im folling .. just got confused by the number that you get multiplied by itself to get 2

Answer 36

like, what is the square root of 4?

Answer 37

2

Answer 38

yes, so the answer to a square root problem looks like this

sqrt(4) = 2*2

Answer 39

in other words, the answer to a square root problem is a number multiplied by itself (in this case, 2)

Answer 40

ok

Answer 41

yes, alright : )

now you see, the square root of 4 can never be negative

Answer 42

because 2*2 = 4 and (-2)*(-2) = 4 also

Answer 43

oooooooohhh!!!!

Answer 44

ok i got it lol

Answer 45

so, the square root function can never have a domain that is negative... simply beacuse it cant ever get there!

Answer 46

alright cool haha hope that helps

try to look at the other basic functions and figure them out if you want. it will help to understand problems a loooot

Answer 47

i would also like to point out, that any time the power is negative

like x^3 or x^5 or x^7 etc.

Answer 48

then, the answer CAN be negative

Answer 49

or woops what i mean is x^1/3 x ^1/5 x^1/7

Answer 50

if the fraction is an odd number (like 3,5,7) then you can get negatives because

(-a)*(-a)*(-a) is actually -(a^3)

Answer 51

in other words, if you multiply a number by itself 3 times, it can be negative

in like in the case of only 2 numbers, which cannot be negative.

Answer 52

hope you understand that, gotta go eat some food enjoy

Answer 53

ok.. thanks .. i think i got it down!! :D .. incase of anything ill ask more questions later.. thank you so much again!!! enjoy getting food!!! have a feast!!! lol