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 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:

$f(x)\text{ = }\frac{1}{x(x-3)}$

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).