To find [tex]\((f - g)(x)\)[/tex] when given the functions [tex]\( f(x) = 3x - 1 \)[/tex] and [tex]\( g(x) = x + 2 \)[/tex], let's follow these steps:
1. Write down the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
f(x) = 3x - 1
\][/tex]
[tex]\[
g(x) = x + 2
\][/tex]
2. To find [tex]\((f - g)(x)\)[/tex], subtract [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex]:
[tex]\[
(f - g)(x) = f(x) - g(x)
\][/tex]
3. Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into the equation:
[tex]\[
(f - g)(x) = (3x - 1) - (x + 2)
\][/tex]
4. Distribute the negative sign and combine like terms:
[tex]\[
(f - g)(x) = 3x - 1 - x - 2
\][/tex]
[tex]\[
(f - g)(x) = 3x - x - 1 - 2
\][/tex]
[tex]\[
(f - g)(x) = 2x - 3
\][/tex]
So, [tex]\((f - g)(x) = 2x - 3\)[/tex].
Therefore, none of the given choices (including "4x + 1") are the correct expression for [tex]\((f - g)(x)\)[/tex]. The correct answer should be:
[tex]\[
(f - g)(x) = 2x - 3
\][/tex]
