Question

(Choose one.)a) all real numbers except 0 and -3b) all real numbers except 0 and 3c) all real numbers between 0 and 3d) all real numbers except 3d) all real numbers

Answer 1

The correct answer is Option d) all real numbers.

Step-by-step explanation:

In this question, we are given a set of options: a) all real numbers except 0 and -3, b) all real numbers except 0 and 3, c) all real numbers between 0 and 3, and d) all real numbers. To determine which option is correct, we need to understand the meaning of each option.

Option a) states that all real numbers are included except 0 and -3.

Option b) states that all real numbers are included except 0 and 3.

Option c) states that all real numbers between 0 and 3 are included.

Option d) states that all real numbers are included.

Based on these explanations, the correct answer is Option d) all real numbers.

Answer 2

The domain of the function is all real numbers except 0 and 3 (option B).

Domains are the inputs in a function. They are also referred to as the x values

The given function:

`f(x)\text{ = }(1)/(x(x-3))`

The domain of the above function are the values of x for which the function would be defined. Hence, values of x that makes the function undefined will not be part of the domain.

To determine the values of x that will make it undefined, we need to equate the denominator to zeroo :

x (x-3) = 0

x = 0 or (x-3) = 0

x = 3

From the above, when x = 0 or x = 3, the function will be undefined. Every other number is defined under the function.

Hence, the domain of the function is all real numbers except 0 and 3 (option B).