Question

what is the domain of f(x)= (Ln x +SQRT [4-x] ) /sinx

Answer 1

Intersect the domains of these component functions :)
Because all of them have to be satisfied.
What's the domain of ln(x) ?

Answer 2

0 ----- 2.

Answer 3

is the answeR: 0>x<4

Answer 4

Nope :)
Now, what's the domain of ln(x) ?

Answer 5

idk...
isnt the smallest 0? and biggest infinity?

Answer 6

smallest is not 0, because 0 is not in the domain.
more like
(0 , infinity)

Okay, great.
Now what about the domain of \(\large \sqrt{4-x}\)

Answer 7

-infinity to 4

Answer 8

so isnt it just 0 to 4?

Answer 9

\((-\infty, 4]\) I'd think

Answer 10

Oay, yes :)
Now, intersect this with the domain of ln(x)
which is (0 , infinity)

Answer 11

*okay

Answer 12

how could it be -infinity .. the ln curve doesnt go that far

Answer 13

Yes it does :D
and it's +infinity and not -infinity....
negative numbers do not go inside the ln :)

Answer 14

uugghhh so @terenzreignz is hte answer 0,4???!!!

Answer 15

Important to include the () or the []
to indicate openness or closedness :)

Answer 16

my -infinity q was for that other person who posted abt -inifinty to 4 being the domain

Answer 17

hehe, ohh right, log can't take negs..

Answer 18

Domain of \(\sqrt{4-x}\) = \((-\infty,4]\).
Domain of \(\ln x\) = \((0,\infty)\).

Find the intersection of these two domains:
\[(-\infty,4]\cap(0,\infty)\]

Answer 19

What is
\[\Large (0,\infty) \cap (-\infty , 4] =\color{red}?\]

Answer 20

FOR CRYING OUT LOUD IS IT (0,4)

Answer 21

oh... I'm late lol :D

Answer 22

hehe

Answer 23

@liliy simply put, no :)
Besides, you still have a sin(x) at the denominator :D

Answer 24

dang

Answer 25

okay... so:(

Answer 26

The intersection should be
\[\large (0,4]\]
because the 4 is included.

Answer 27

sin(x) =0 when x=2pi

Answer 28

so, there are really 3 restrictions on the domain, 2 on the numerator and 1 on the denominator

Answer 29

Yup, what @jdoe0001 said :D
and since our tentative domain is already (0,4]
then we really couldn't care less about 0 or 2pi, since...
\[\Large 2\pi \approx 6.28\]
which is already well beyond the boundaries of (0,4]
and 0 simply is not included in (0,4]

XD

Answer 30

\((-\infty, 4]\) restriction doesn't apply however to the ln() function, so the infinity holds

Answer 31

However, there IS nother value which would make sin(x) equal to zero, that is well within (0,4], have you spotted it yet, @liliy ? :)

Answer 32

another*

Answer 33

pi