Question

Identify the restrictions on the domain of f(x) = quantity x plus 2 over quantity x minus 3.

x ≠ −2
x ≠ 2
x ≠ −3
x ≠ 3

Answer 1

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:

**\( x \neq 3 \)**.