Analyzing the Rational Function: Determine the Domain of (5-x)/(2-x)

To determine the domain of the function $\frac{5-x}{2-x}$, we need to identify and exclude any values of $x$ that make the function undefined. This occurs when the denominator equals zero.

• Step 1: Set the denominator equal to zero:
  $2-x = 0$
• Step 2: Solve for $x$:
  Adding $x$ to both sides gives $2 = x$. Hence, $x = 2$.

This means that the function is undefined when $x = 2$. Therefore, the domain of the function consists of all real numbers except $x = 2$.

Thus, the domain is: $x \ne 2$.

The correct answer choice is:

Yes, $x\ne2$