Question

Given that f(x)=x2−5x+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 first need to understand what the function \( (fg)(x) \) means. It involves the multiplication of the functions \( f(x) \) and \( g(x) \).

The functions are defined as follows:

\[
f(x) = x^2 - 5x + 6
\]

\[
g(x) = x - 2
\]

The domain of the composite function \( (fg)(x) \) is determined by the domains of both functions.

1. **Finding the domain of \( g(x) \)**:
The function \( g(x) = x - 2 \) is defined for all real numbers. There are no restrictions.

2. **Finding the domain of \( f(x) \)**:
The function \( f(x) = x^2 - 5x + 6 \) is also defined for all real numbers, as it is a polynomial.

However, when creating the product \( (fg)(x) \), we need to consider any restrictions due to the multiplication of the functions. Specifically, we must check if \( g(x) \) can be zero because division by zero is undefined.

Set \( g(x) = 0 \):

\[
x - 2 = 0
\]

Solving this gives us:

\[
x = 2
\]

Thus, \( x = 2 \) will make \( g(x) \) equal to zero, which means \( (fg)(x) \) is undefined at this value.

Therefore, the value of \( x \) that must be excluded from the domain of \( (fg)(x) \) is:

\[
\boxed{2}
\]