To find the value of \( x \) that must be excluded from the domain of \( (fg)(x) \), we need to understand the composition of functions \( f \) and \( g \).
The functions are given as:
- \( f(x) = x^2 - 5x + 6 \)
- \( g(x) = x - 2 \)
The expression \( (fg)(x) \) means we are multiplying the two functions: \[ (fg)(x) = f(x) \cdot g(x) \]
However, since the function \( g(x) \) appears in the multiplication, we must determine when \( g(x) = 0 \) because the multiplication would yield an undefined result in the context of division or composition involving \( g \).
Set \( g(x) = 0 \): \[ x - 2 = 0 \] Solving this gives: \[ x = 2 \]
So, the value of \( x \) that must be excluded from the domain of \( (fg)(x) \) is: \[ \boxed{2} \]
1 answer