Question

Can anyone show me the steps and answer?

Answer 1

Answer:

  (-∞, 3) ∪ (3, 4) ∪ (4, ∞)

Step-by-step explanation:

Steps:

1. Read and understand the question. Here, you're being asked for the domain of a rational function, one with a 2nd-degree polynomial in the denominator. The domain is the set of x-values for which the function is defined.

2. Understand that the function will be undefined when the denominator is zero, so to answer the question, you must find the values of x that make the denominator zero.

3. Use any of the methods you have been taught to determine the zeros of the denominator polynomial. For this one, it is convenient to factor it:

  x² -7x +12 = (x -3)(x -4)

The values of x that make this zero are 3 and 4, so these values are excluded from the domain.

4. Write an expression in interval notation that includes all real numbers except 3 and 4. That is, you want to translate this to interval notation:

  (-∞ < x < 3) ∪ (3 < x < 4) ∪ (4 < x < ∞)

Using what you know about interval notation, you write it as ...

  (-∞, 3) ∪ (3, 4) ∪ (4, ∞)