Question

find domain:

f(x)=x+1/x-2

(can you explain and help me understand how to do this?)

Answer 1

is the denominator just 'x' or is it 'x-2' ?

Answer 2

x-2

Answer 3

The denominator is likely x-2.

Answer 4

you CANNOT divide by zero

if the denominator were zero, then

x-2=0

x = 2

so that means if x = 2, then the denominator is zero

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to avoid division by zero, you have to exclude x = 2 from the domain. Any other number is allowed in the domain

so that's why the domain is the set of all real numbers x, but x cannot equal 2

Answer 5

I dont really get it
Can you give me some sort of steps so I know what to do?
I have an entire worksheet on this.

Answer 6

you set the denominator equal to zero, then solve for x

this solution you get for x is the value you kick out of the domain (everything else stays in the domain)

Answer 7

x - 2 = 0

x = 2

therefore the only thing you exclude from the domain is x = 2

Answer 8

again you're doing this because division by zero is not allowed and it's undefined

Answer 9

But isnt this about the function, not solving for x?

Answer 10

yes it is about the function since domains apply to functions (specifically, the input of a function)

Answer 11

the domain is the set of all allowed inputs of a function

ie...the set of allowed x values

Answer 12

everything is allowed BUT 2 since 2 causes a division by zero error

Answer 13

i am so confused and frustrated

Answer 14

let's do another example

Answer 15

ok

Answer 16

let's say we have the function

f(x) = 1/(x+7)

the "x+7" is all in the denominator

----------------------------------

again we cannot divide by zero, so x+7 cannot be zero

if it were, then x+7 = 0 turns into x = -7 after we solve for x

so x = -7 makes the denominator zero and we have to kick x = -7 out of the domain (to avoid division by zero)

so the domain of this function is the set of all real numbers but x cannot equal -7

Answer 17

im sorry but i am still so confused

Answer 18

where are you stuck?

Answer 19

I just cant seem to grasp it. We have done this in class a billion times, but I am not remembering how to do this.

Answer 20

I am not sure how you got to the answer. Can you put it in some sort of step form?

Answer 21

I laid out all the steps and the answer. You set the denominator equal to zero, then you solve for x. After getting your solution(s), you know what to kick out of the domain of all real numbers.

Answer 22

This is the answer I found online:
x≠1
(−∞,1) U (1,∞)

Answer 23

oh so you're not sure how to go from x≠1 to (−∞,1) U (1,∞)

btw that's not the answer, but it's close

Answer 24

Im not sure how to do any part of this problem. I just got that answer from using mathway

Answer 25

does my explanation make any sense at all?

Answer 26

no
maybe I have a learning disorder

Answer 27

do you agree that division by zero is not allowed or not defined

Answer 28

yes

Answer 29

example: 1/0 is NOT defined

Answer 30

ok

Answer 31

so that means we must make sure that the denominator is NOT zero

Answer 32

IF the denominator were zero, then we'd have problems

so that's why we have to set the denominator equal to zero, then solve for x to figure out which value or values of x make the denominator zero

making sense?

Answer 33

but dont we just want the domain of the function

Answer 34

yes we do, but it turns out that the domain of rational functions hinges on the denominator (because of this division by zero error)

Answer 35

normally any number would work, BUT because of this division by zero error, we have to check to see which values of x make the denominator zero

any we find must be excluded from the domain

Answer 36

your words are too complicated. I am not as smart as you.

Answer 37

Thank you for your help, but I do not think I will understand this ever.

Answer 38

don't give up on it, take a break for a bit, but come back when you feel ready again

Answer 39

I just dont see how people understand this

Answer 40

you will soon, trust me

Answer 41

just try to approach it from a different angle if you have to

Answer 42

how? No one can help me right now. My dad does not know math. My sister does not know this.

Answer 43

ok so you agree that something like 1/0 is not allowed, so far so good

if we had the expression 1/x, what value of x is NOT allowed?

Answer 44

Nothing because it is not 0

Answer 45

so x = 0 is allowed? or no?

Answer 46

no

Answer 47

good, x = 0 is NOT allowed in 1/x since 1/0 is not allowed

Answer 48

so the domain of 1/x is


x≠0
(−∞,0) U (0,∞)


those are two fancy ways of saying "everything is allowed but 0"

Answer 49

does that make sense?