To find [tex]\((f - g)(x)\)[/tex] for the given functions [tex]\( f(x) = 3x - 5 \)[/tex] and [tex]\( g(x) = x + 3 \)[/tex], we need to subtract [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex].
First, let's express [tex]\((f - g)(x)\)[/tex] in general form:
[tex]\[
(f - g)(x) = f(x) - g(x)
\][/tex]
Now, substitute [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into this expression:
[tex]\[
(f - g)(x) = (3x - 5) - (x + 3)
\][/tex]
Next, we'll distribute the negative sign and simplify the expression:
[tex]\[
(f - g)(x) = (3x - 5) - x - 3
\][/tex]
Combine like terms:
[tex]\[
(f - g)(x) = 3x - x - 5 - 3
\][/tex]
[tex]\[
(f - g)(x) = 2x - 8
\][/tex]
So, the simplified form of [tex]\((f - g)(x)\)[/tex] is:
[tex]\[
2x - 8
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{2x - 8}
\][/tex]
Thus, the correct option is:
[tex]\[
\boxed{C}
\][/tex]
