how to find domain of a function

[short junco]

pls

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[winter mica]

well domain is just for what x values is it defined

so what kind of function do you have

[short junco]

wcydm

[fluid tulip]

Code0of

[short junco]

i dont get how to find it

and what does it mean

[cerulean ember]

here for any value fo x u get a value from function so the domain is (-inf, inf)

or you can say domain is all real numbers

[short junco]

what

so all real values of x

[winter mica]

so like

if you plug in a value of x

does the function return a value

[short junco]

it always will

unless its undefined

[winter mica]

not necessarily

[short junco]

how

[winter mica]

$\sqrt{x}$

[fluid tulip]

!𒐪 ɹɐupoɯ⇂ㄥ8𝟝 𒐪!

[short junco]

yeah well a square root wont work

can u tell me it simplified

i dont understand how to find it

do i just plug in random x values

[winter mica]

uhh well I think the only two reasons for the domain being not all reals is just

dividing by 0

or a square root function

[winter mica]

@cerulean ember do you know of any others

[short junco]

how would i know if this is all read values of x

[winter mica]

because any real value of x works?

[winter mica]

^

[short junco]

well x could be square root

[cerulean ember]

see when you input any value for x in the function you get a real output

[short junco]

or 0

so if x was square root it would still work

[winter mica]

that still gets a value

(1+sqrt5)^2 exists

[short junco]

then it will always be all real values of x

true

if u can plug in any value

i dont get how to find out

[winter mica]

^^

or like you have a function that’s a circle or something but

that isn’t a real function

[cerulean ember]

1/(x+2) u cant have x = -2

[winter mica]

yea dividing by 0

oh right log functions

log/ln functions can’t have non positive x

[cerulean ember]

To figure out the domain of a function, look at the values of x that make the function work by avoiding situations where you'd divide by zero, making sure square roots have non-negative input, and paying attention to any other operations with particular rules

( f(x) = \frac{1}{x - 3} )

[fluid tulip]

Irshad

[cerulean ember]

take this as an example

1. Avoid Division by Zero

Set (x - 3) not equal to zero and solve for (x): (x - 3 \neq 0).
Solve for (x): (x \neq 3).

[fluid tulip]

Irshad

[cerulean ember]

2. Domain:

The domain is all real numbers except x = 3

The function is defined for any real number x except when x is equal to 3 because that would make the denominator zero.

[winter mica]

@short junco ^

[cerulean ember]

@short junco hope this helps you i made it on a short note but let me know if you still have doubts

[cerulean ember]

@winter mica can you just cross check if what i wrote is correct ty

[jovial crow]

@cerulean ember has given 1 rep to @winter mica