Question

Given that f(x)=x^2−5x+6
and g(x)=x−2
, what value of x
must be excluded from the domain of (fg)(x)
?(1 point)
The value of x
that must be excluded from the domain of (fg)(x)
is x=
.

Answer 1

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:
\[
\boxed{2}
\]