Question

Determine the domain of the function, and choose the correct interval and inequality notations,

Answer 1

Answer:

• See below

Explanation:

Determining the domain of the function P(x) = 2x + 8 is very trivial and does not require the uses of separate intervals.

The domain of a function is the set of input values (x) for which the function is defined. Thus, the domain of P(x) = 2x + 8 is all the real number, which in interval notaion is:

• (- ∞, ∞)

The symbol ∞ is used to indicate that there is not limit for the value of x: it can goe from any negative number to any positive number).

For didactic purposes let's determine the domain of the function

P(x) = 2/(x+8).

In this case, the function is not defined when the denominator equals 0.

Then, the domain excludes the values for which x + 8 = 0.

• x + 8 = 0 ⇒ x = - 8.

Then, the solution is all the real numbers different to - 8.

In interval notation it is:

• (- ∞, -8) ∪ (-8, ∞)

In form of inequaliy that is:

• x < - 8 ∪ x > - 8

That means, all the real numbers less than - 8 and all the real numbers greater than 8.