Question

Determine the domain of the funciton h(x) = 4x/x(x2-16)

Answer 1

the domain are all valid x values

Normally you say x is all real numbers except, and list the "bad" or excluded values.

You will want to exclude any x value that causes a divide by 0
(divide by 0 is not allowed)

Answer 2

Ok so Im looking at {x | x = 4}

Answer 3

{x | x = 4}
means the domain is x=4

x can be a lot of numbers that don't cause you to divide by 0

Answer 4

Ik Im looking at b the one with the + looking

Answer 5

Cause C and D are excluded because of the 0s

Answer 6

those are ≠ meaning not equal
for example the first answer
{ x | x ≠ 4 } means
the domain is all real numbers such that x does not equal 4
another way to say this is
the domain is all real numbers except x=4 (x=4 is excluded)

what numbers cause a divide by 0 in your expression
those are the numbers you want to have x≠ to

Answer 7

The notation is a bit confusing, but what you want to say is
{ x | list of x ≠ values }
where the list are the values that you want to exclude (because they cause a divide by 0)

Answer 8

Ok still alittle confused but am I wright on b since it i what you explained and the answers divided by 0 are excluded so that leaves a or b

Answer 9

I think you are missing the idea.

First, do you know what x values cause a divide by 0 in
4x/x(x2-16)

Answer 10

I do not

Answer 11

you have
\[ \frac{4x}{x(x^2-16)} \]
you do not want the bottom to be zero. What x values cause the bottom to be 0 ?
you can set up an equation
\[ x(x^2-16) =0 \]
you can factor the x^2 - 16 (it is a difference of squares) into (x-4)(x+4)
you have
\[ x(x-4)(x+4)=0 \]
now if any of the 3 terms is 0, you will end up with the bottom being 0
what 3 x values cause the bottom to be 0 ?

Answer 12

For example, if x=0 in
\[ x(x-4)(x+4) \\ 0(0-4)(0+4) \\ 0\cdot -4 \cdot 4 =0 \]

Answer 13

what makes (x-4)= 0 ?
what makes (x+4)= 0 ?

Answer 14

Im sorry im so lost this is my 3rd day into the subject thats why im asking to pretty much solve this step by step so I can get it for the others I have to do I kind of get it,

Answer 15

can you answer
what x value makes (x-4)= 0 ?

Answer 16

It would have to be 4

Answer 17

yes. you could use algebra to "solve for x"
x-4= 0
add +4 to both sides
x-4+4= 0+4
simplify, (remember -4 + 4 is 0
x = 4

what that means is that the bottom
x ( x-4) (x+4)
will, if we make x=4, become
4 * (4-4) * (4+4)
which is 4*0*8
and the times 0 will make the whole thing 0.

so x=4 is on the "exclude list"
we also have x=0 on the exclude list

now, what x makes
x+4 = 0
?
we will want to exclude that value also

Answer 18

I ran out of time to finish the practice it ended up being c

Answer 19

yes, x+4=0 means x= -4 will make the bottom 0

so the domain is all x but x≠-4, x≠0, x≠ 4
which reads: all x, but x is not equal to -4, not equal 0, and not equal to 4
they write it this way
{ x | x≠-4, x≠0, x≠ 4 }

Answer 20

The idea in these problems is not allow any x value that makes the bottom 0, because divide by zero is not allowed

if there is a square root, no x value that makes a negative number inside the square root is allowed.