Question

Identify the restrictions on the domain of f(x) = (x - 3) / (x + 2).

1) x ≠ -3
2) x ≠ -2
3) x ≠ 2
4) x ≠ 3

Answer 1

The restriction on the domain of the function f(x) = (x - 3) / (x + 2) is that x cannot be -2, to prevent division by zero.

Step-by-step explanation:

The student has asked to identify the restrictions on the domain of f(x) = (x - 3) / (x + 2). For a function to be defined, the denominator cannot be equal to zero because division by zero is undefined. The denominator of this function is x + 2. Therefore, the value of x that would make the denominator zero is -2. So the correct restriction on the domain of this function is that x cannot equal -2 to avoid division by zero.

The restrictions on the domain for the function f(x) = (x - 3) / (x + 2) is x ≠ -2, which corresponds to option 2 from the choices given.