Question

f(x)=x-2/x^3-2x^2-9x+18 find domain

Answer 1

When you see division REMEMBER: NO DIVIDE BY ZERO

in this case, where you have
x^3-2x^2-9x+18
find all the values of x that make it zero. Solve
x^3-2x^2-9x+18=0

this is cubic (highest power is 3) so there are 3 values for x (may be repeated, 2 may be complex) that would make it zero, so are not allowed i.e. not in the domain

Answer 2

how will I understand this concept? I m not getting any thing?

Answer 3

do you understand
f(x)= x (a very simple function)

for every x, you figure out f(x) (here f(x) is just x)
all x will work, so the domain is all real numbers

Answer 4

ook .

Answer 5

so all the values with x are function of x

Answer 6

a function of x means: given a number (called x) calculate f(x) using that number. Do not over think it. f(x) is defined by a "rule" like f(x)= 2*x+1 or
x*x +3, and so on.

Answer 7

ohhh so fx is the x

Answer 8

Now sometimes the rule for f(x) does not work for some x's
you know 1/0 is undefined, right? so dividing by 0 is not allowed.

if you have a function like
f(x)= 1/x
this will work for any x except x=0. at x=0 f(x) is undefined. We do not want undefined values, so we exclude x=0. we say the domain is all real numbers except 0

Answer 9

ok . so f(x)=x-2/x^3-2x^2-9x+18 how we end up with an answer x not equal to -3? and x =2?

Answer 10

what is the bottom of that when x=2 ?

Answer 11

no I mean x not equal to 2 and 3?

Answer 12

x/xnot equal to 3 x/x not equal to 2?

Answer 13

I know what you mean.
what is the bottom of that when x=2 ?

in other words, what is
x^3-2x^2-9x+18
when you replace x with 2?

Answer 14

then I have to calculate and might be come up with some number

Answer 15

yes

Answer 16

so x has to be 0?

Answer 17

I donot suppose to come up with any number?

Answer 18

what is
x^3-2x^2-9x+18
when you replace x with 2?

Answer 19

(2)^3-2(2)^2-9(2)+18

Answer 20

yes, but what number is that?

Answer 21

8-8-18+18

Answer 22

0

Answer 23

that is the crucial fact. because
f(x)=x-2/x^3-2x^2-9x+18 with x=2 gives you
\[ f(0)= \frac{0}{0} \]
and that is indeterminate (an undefined number). We do not want undefined numbers for f(x). So the way to deal with it is say x=2 NOT ALLOWED

same for the other x values (x= 2, x=3, x=-3 not allowed) that make the bottom 0. NO DIVIDE BY ZERO allowed, so don't allow those x values.

Answer 24

ahan. so x should not be equal to 0 . so to find the domain do we have to first find it with 0, then 1 and then 2 to find out if the answer is 0 or not?

Answer 25

so x should not be equal to 0 NOT QUITE

You do not what to end up dividing by zero. if you had
\[ f(x)= \frac{1}{x-1} \]
you do not want x=1 because 1-1=0 and you end up dividing by zero

So to answer your question: set the denominator = 0
and solve for all x that make it zero. Those are the x's we do not allow.

for your problem:
x^3-2x^2-9x+18=0
find all x that make this equation true. Those are the "bad x's"

This is a hard problem. But if they give you numbers, you can try them and see if any are "bad"

Answer 26

so for each question if they donot have given use the values so I have to kep putting values 0, 1 2 3 to find the bad x

Answer 27

Guessing might work.... But hopefully the problems they are giving you are "easy" because they are teaching the idea of domain (all "good" x's, no "bad x's")
so I hope they don't give hairy problems where it's very difficult to find the "zeros"

Post another question....

Answer 28

so I just guess and write? becuase there is no value of x given

Answer 29

which problem?

Answer 30

this one and others like that?

Answer 31

becuase how far I can go to keep finding bad and goodx

Answer 32

post the next question