The function g is defined below.
g(x)=((x)^(2)-9x+14)/((x)^2-11x+24)
Find all values of x that are NOT in the domain of g.
If there is more than one value, separate them with commas.
we cannot divide by zero, so the denominator cannot be zero
when is x^2 - 11x + 24 = 0 ?
(x-3)(x-8) = 0
x =3 or x = 8
so x cannot be 3 or 8
Thanks!
To find the values of x that are not in the domain of g(x), we need to look for any values of x that make the denominator of the fraction equal to zero.
The denominator of g(x) is (x^2 - 11x + 24).
Let's solve the equation x^2 - 11x + 24 = 0 for x using factoring or quadratic formula.
Factoring:
(x - 3)(x - 8) = 0
Setting each factor equal to zero:
x - 3 = 0, so x = 3
x - 8 = 0, so x = 8
Therefore, the values of x that make the denominator zero are x = 3 and x = 8.
These values make the denominator undefined since division by zero is not allowed.
So, the values of x that are NOT in the domain of g are x = 3 and x = 8.
To find the values of x that are not in the domain of the function g(x), we need to identify any values that would cause a division by zero or create undefined results.
In this case, the function g(x) is a rational function (a fraction), and the denominator should not equal zero. So we can start by finding the values of x that make the denominator zero.
Let's solve the equation (x^2 - 11x + 24) = 0 to find the values of x that make the denominator zero:
Factor the quadratic equation:
(x - 3)(x - 8) = 0
Setting each factor equal to zero, we have:
x - 3 = 0 or x - 8 = 0
Solving for x, we get:
x = 3 or x = 8
These are the values of x that make the denominator zero, which means they are not in the domain of g(x). Therefore, the values of x that are NOT in the domain of g are x = 3 and x = 8.