Domain of g(x) = (x-2)/(x^2-9) |x|≠3

In summary, the domain of the function g(x) = (x-2)/(x^2-9) is all real numbers except for x = 3 and x = -3, due to the possibility of division by zero. The notation |x|≠3 indicates that the absolute value of x cannot equal 3 in order for the function to be continuous. X = -3 is also not included in the domain for the same reason as x = 3. There are no other restrictions in the domain of g(x) as long as x is not equal to 3 or -3.
  • #1
alpha01
77
0
for g(x) = (x-2) / (x^2 -9)

the domain of the function would be simply to have the denominator not equal to 0, which in this case would be x = 3.

but.. the solution states that it is -3 and 3 cannot be used.

this is confusing seeing that -3^2 -9 = -18 which is not 0.

maybe it means |-3|?
 
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  • #2
(-3)^2 - 9 = 9-9 = 0

there is a difference,

-3^2 = (-1)*3^2 = -1*9 = -9, but (-3)^2 = (-1*3)^2 = (-1)^2 * 3^2 = 1*9 = 9
 
  • #3
i get it. thanks
 

What is the domain of the function g(x) = (x-2)/(x^2-9) |x|≠3?

The domain of a function is the set of all possible values that the independent variable (x) can take on. In this case, the domain of g(x) is all real numbers except for x = 3 and x = -3, since these values would result in a division by zero.

Why is x = 3 not included in the domain of g(x)?

When x = 3, the denominator of the function g(x) becomes 0, which is undefined in mathematics. Therefore, x = 3 is not included in the domain to avoid any division by zero errors.

What does |x|≠3 mean in the domain of g(x)?

The notation |x|≠3 means that the absolute value of x cannot equal 3. This is to ensure that the function g(x) is continuous and does not have any breaks or jumps in its graph.

Can I include x = -3 in the domain of g(x)?

No, x = -3 is also not included in the domain of g(x) because it would result in a division by zero, just like x = 3. The absolute value notation |x|≠3 applies to both positive and negative values of x.

Are there any other restrictions in the domain of g(x)?

No, there are no other restrictions in the domain of g(x). As long as x is not equal to 3 or -3, the function g(x) is well-defined and can be evaluated for any other real number values.

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