Question

the function g is defined below.
$g(x)=\frac{x^{2}-13x+42}{x^{2}-36}$
find all values of x that are not in the domain of g.
if there is more than one value, separate them with commas.
$x = $

Explanation:

Step1: Identify undefined condition

A rational function is undefined when its denominator equals 0. Set the denominator equal to 0:
$x^2 - 36 = 0$

Step2: Solve the quadratic equation

Rewrite the equation as a difference of squares:
$(x-6)(x+6) = 0$
Set each factor equal to 0:
$x-6=0 \implies x=6$
$x+6=0 \implies x=-6$

Answer:

$x = -6, 6$