If [tex]$f(x) = 3x - 5$[/tex] and [tex]$g(x) = x + 3$[/tex], find [tex][tex]$(f-g)(x)$[/tex][/tex].

A. [tex]$8 - 2x$[/tex]
B. [tex]$2x - 2$[/tex]
C. [tex][tex]$2x - 8$[/tex][/tex]
D. [tex]$4x - 2$[/tex]



Answer :

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]