Question

identify the restrictions on the domain of $f(x) = \frac{x + 5}{x - 2}$. \
\
$\circ$ $x \
eq 5$ \
\
$\circ$ $x \
eq -5$ \
\
$\circ$ $x \
eq 2$ \
\
$\circ$ $x \
eq -2$

Explanation:

Step1: Recall domain restriction for rational functions

For a rational function \( f(x)=\frac{g(x)}{h(x)} \), the denominator \( h(x) \) cannot be zero (since division by zero is undefined).

Step2: Set denominator equal to zero and solve

Given \( f(x)=\frac{x + 5}{x - 2} \), set the denominator \( x - 2 = 0 \).
Solving \( x - 2 = 0 \), we add 2 to both sides: \( x = 2 \).
So, \( x \) cannot be 2 (i.e., \( x
eq2 \)) to avoid division by zero.

Answer:

x ≠ 2