Question

What is the domain of the rational function f of x is equal to the quantity x squared minus x minus 12 end quantity over the quantity x cubed minus 4 times x squared minus 4 times x plus 16 end quantity question mark

{x ∈ ℝ| x ≠ –2, 2, 4}
{x ∈ ℝ| x ≠ –2, 2}
{x ∈ ℝ| x ≠ –3, 4}
{x ∈ ℝ| x ≠ –3, –2, 2, 4}

Answer 1

The domain of the rational function is:

{x ∈ ℝ| x ≠ –2, 2}

What is the domain of the rational function?

Here we have the rational function:

$f(x) = \frac{x^2 - x - 12}{x^3 - 4x^2 - 4x + 16}$

We want to get the domain of that function. First, we can rewrite the numerator and denominator as:

$x^2 -x - 12 = (x + 3)*(x - 4)$

$x^3 - 4x^2 - 4x + 16 = (x - 4)*(x + 2)*(x - 2)$

Then we can rewrite the rational function as:

$f(x) = \frac{(x + 3)*(x - 4)}{(x - 4)*(x + 2)*(x - 2)}$

This can be simplified to:

$f(x) = \frac{(x + 3)}{(x + 2)*(x - 2)}$

Now, the domain will be the set of all real numbers, minus the values of x that generate problems.

In this case, the values:

x = -2 and x = 2 make the denominator to be zero, and we can't divide by zero, so  we conclue that the domain is:

{x ∈ ℝ| x ≠ –2, 2}

If you want to learn more about rational functions:

https://brainly.com/question/1851758

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