Question

Find all values of x that are NOT in the domain of g.
If there is more than one value, separate them with commas

g(x) = x^2 - 9x +18 / x^2 -4

Answer 1

Answer:

x=2,-2 are NOT in the domain of given function

Step-by-step explanation:

The domain consists of all the values of input that doesn't make the result approach to infinity. As the given function is a rational function, division by zero will lead to infinity so we have to find the numbers which will make the denominator equal to zero.

So,

putting the denominator equal to zero

$x^2-4 = 0\\x^2 = 4\\\sqrt{x^2} = \sqrt{4}\\x = 2, -2$

X=2 and x=-2 will make the denominator zero and the function will lead to infinity so

x=2,-2 are NOT in the domain of given function ..

Answer 2

The values for x=2 and x= -2 are not in the domain of the given equation g(x).

Domain and Range

The domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined.

While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

The given equation ( $g(x) = \frac{x^2 - 9x +18}{x^2 -4}$ ) is a fraction with variable x in the numerator and the denominator.  For the numerator, there are not any restrictions, but for the denominator there is one. The denominator of a fraction can not equal zero.

Therefore,

x²-4$\neq$0

x²$\neq$4

x$\neq$$\sqrt{4}$

x$\neq$ ±2

Thus, x=2 and x=-2 are not in the domain of g.

Learn more about the domain here:

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