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 need to analyze the functions \( f(x) \) and \( g(x) \).

The function \( g(x) = x - 2 \) is defined for all real numbers. Therefore, it does not impose restrictions on the domain.

Now, \( (fg)(x) \) is defined as the product of the two functions, \( f(x) \cdot g(x) \).

Since \( f(x) \) is a polynomial \( f(x) = x^2 - 5x + 6 \), it is also defined for all real numbers.

However, if \( g(x) \) is used as the denominator in a rational function, we would need to exclude the value that makes \( g(x) = 0 \) since division by zero is undefined.

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

\[
x - 2 = 0 \implies x = 2
\]

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

\[
\boxed{2}
\]