To find the value of \( x \) that must be excluded from the domain of the function \( (fg)(x) \), we need to check the definitions of the functions \( f(x) \) and \( g(x) \).
Given:
- \( f(x) = x^2 - 5x + 6 \)
- \( g(x) = x - 2 \)
The function \( (fg)(x) \) represents the product of \( f(x) \) and \( g(x) \), which can be expressed as: \[ (fg)(x) = f(x) \cdot g(x) = (x^2 - 5x + 6)(x - 2) \]
In this case, we need to determine if \( g(x) = x - 2 \) has any restrictions. The function \( g(x) \) is a polynomial and is defined for all real numbers, so it does not impose any restrictions on the domain.
However, we should note that if the expression for \( g(x) \) equals zero, then it could lead to a situation that must be excluded since it indicates a point of discontinuity (not applicable for multiplication, but generally important for divisions or roots). When \( g(x) = 0 \): \[ x - 2 = 0 \implies x = 2 \]
Thus, despite \( (fg)(x) \) being defined for all \( x \), special attention must be given if it involved division. But since this is a multiplication, the result can still be calculated at that point.
Observing \( g(x) \), the critical value here is when \( g(x) = 0 \) at \( x = 2 \), so the final conclusion, in terms of generic considerations, would have been \( x = 2 \).
Final Answer: The value of \( x \) that must be excluded from the domain of \( (fg)(x) \) is \( x = 2 \).