To identify the restrictions on the domain of the function \( f(x) = \frac{x + 2}{x - 3} \), we need to look for values of \( x \) that would make the function undefined. This happens when the denominator is equal to zero.
The denominator of the function is \( x - 3 \). Setting the denominator equal to zero, we solve for \( x \):
\[ x - 3 = 0 \] \[ x = 3 \]
This means that the function \( f(x) \) is undefined when \( x = 3 \). Therefore, the restriction on the domain is:
\[ x \neq 3 \]
The other values you provided (−2, 2, and −3) do not produce any restrictions on the domain of this specific function.
Thus, the correct restriction on the domain of \( f(x) = \frac{x + 2}{x - 3} \) is:
\( x \neq 3 \).