Find the largest domain for the following function: g(x) = (x^2 - 10)/3x^2 - 12what is the largest domain of this function

In this case, the denominator of the function impose the
domain of definition.

We'll impose the constraint of
existence of the function:

3x^2 - 12 different
from 0

In other words, the domain of definition will
contain x values that don't cancel the denominator.

We'll
compute the roots of the equation

3x^2 - 12 =
0

We'll divide by 3 both
sides:

x^2 - 4 = 0

Since it is
a difference of squares, we'll write it using the
formula:

a^2 - b^2 =
(a-b)(a+b)

x^2 - 4 =
(x-2)(x+2)

But x^2 - 4 = 0,
so

(x-2)(x+2) = 0

We'll put
each factor as 0:

x - 2 = 0

x
= 2

x + 2 = 0

x =
-2

The domain of definition is the real set
R, rejecting the roots of the equation from
denominator.

R - {-2 ;
+2}