Find the domain of the function (f/g) (x), given f(x) = x^2 - 3x - 10 and g(x) = x^2 - 4

We want to find the domain of the rational function (f/g)(x), we will see that the domain is {x | x ≠ 2 or -2}

We start by assuming that the domain is the set of all real numbers, and then we remove the problematic points.

For example, in this case, problematic points are these that make the denominator equal to zero.

We have:

f(x) = x^2 - 3x

g(x) = x^2 - 4

The denominator is zero when g(x) = 0, then the problematic points are the solutions of:

x^2 - 4 = 0

x^2 = 4

x = ± 2

Then the domain must be all real values of x except x = 2 and x = -2

So the domain is written as:

{x | x ≠ 2 or -2}

If you want to learn more about domains, you can rad:

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Step-by-step explanation:

(x)

= ← factor numerator/denominator

= =

The removal of the factor (x + 2) means there is a removable discontinuity (hole) at x = - 2

the denominator of cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that x cannot be.

solve x - 2 = 0 ⇒ x = 2

Therefore x ≠ - 2, 2

domain is {x|x≠ - 2 or 2 }