Question

May someone please explain to me with a step by step process on how to solve this equation?
Thank you.

Find the domain of the function
\[g(x)=\frac{ 3 }{ x-4 }\]

I don't know how to solve this.

Answer 1

much as i hate it, there ARE rules when it comes to working with numbers :/

Answer 2

one of them being... you CANNOT divide by zero.

Answer 3

First of all, you have to know what's a domain.

Answer 4

now a domain is the set of all values that x is 'allowed' to assume.

since the operation here in question is 'division', the only values x ISN'T allowed to take is that which would give a division by zero, aye? ^.^

Answer 5

...hmmm
...well
...ready when you are, Angel ^.^

Answer 6

Sorry everyone, something happened with my router >.< but I'll read the comments now

Answer 7

What exactly do you mean by "the only values x ISN'T allowed to take is that which would give a division by zero"

I'm a little confused with that

Answer 8

set the denominator equal to zero
solve for\(x\)
then say "all real numbers except that one"

Answer 9

or in other words... the value of x that would cause a division by zero is the one value of x that isn't allowed...

So... what value of x would make the denominator zero?

Answer 10

I am so sorry but I am sooooo confused right now >.< I know nothing of what you all are speaking of. I wanna say... 0...but isn't anything divided by 0 a guaranteed 0 anyways >.<

Answer 11

oh heck no :D

that problem's been troublesome for centuries... but

think of it this way...

A hundred divided by fifty is 2.
divided by twenty-five is 4
divided by twenty is 5
divided by ten is 10
divided by five is 20
divided by four is 25
divided by two is 50
divided by one is 100
...
divided by half is 200
divided by a quarter is 400

and so on

as the divisor gets smaller and smaller, the quotient gets bigger and bigger...

so what about zero?

how many times can you take away zero from a number?

Infinite?

lol
confusing

that's why it isn't allowed ;)

Answer 12

I think I kinda understand that... o.o but what does dividing by 0 have to do with this equation? Is it because the x is in the denominator?

Answer 13

Yes. We want to find the value of x that results in division by zero... which means THAT value of x isn't allowed.

Answer 14

I want to say 0 times but I feel like the answer to that isn't so simple lol ... I'm not sure exactly how one would find that answer because I tried a bunch of numbers divided by 0 and got ERROR then I tried 0 divided by a bunch of numbers and got 0...so I'm not sure...how to come up with that...

Answer 15

x-0 is 5?

Answer 16

division isn't commutative, Angel :)
0 divided by any (nonzero) number is zero, true, but
any number divided by zero... well, it's not defined, so...

Answer 17

v.v r.i.p. to my mind.

Answer 18

look... no need to go into details right now... just find the value of x that makes the denominator (x-4) equal to zero...

x - 4 = 0

x = ?

Answer 19

4? o.o

Answer 20

yup.

So the domain is ALL real numbers EXCEPT 4.

Because 4 results in division by zero, which isn't allowed.

Get it? ^.^

Answer 21

oooohhhh so if it was x - 30 = 0 then the domain would be all real numbers with 30 excluded? e.O

Answer 22

if it was x-30 in the denominator, yes.

Answer 23

I think I get that part now >.<

Answer 24

great.
bye :P

Answer 25

thank youuuuu