Question

Study the function below and then answer the questions that follow.

What is the domain of f(x)?


What is the range of f(x)?

Answer 1

Domain: all real values of x except -2

Range: y > -4

Explanation:

Domain: union of all intervals of x

x < -2 U -2 < x < 0 U x》0

This includes all real values of x except x = -2

When x < -2

-x - 2 > 0

When -2 < x < 0

-4 < -x² < 0

When x》0

x》0

Range is the union of all these outputs

y > 0 U -4 < y < 0 U y》0

y > -4

Answer 2

Answers and Step-by-step explanations:

Notice that -2 is not included in the inequality, but any other number is. That means that the domain is all real numbers except x = -2.

For the range, I recommend you draw a graph (see the attachment).

As can be seen, the range will be y > -4.

Hope this helps!