To solve the problem, we need to determine [tex]$(f - g)(x)$[/tex], where:
[tex]\[ f(x) = 6x - 8 \][/tex]
[tex]\[ g(x) = -5x + 2 \][/tex]
The operation [tex]$(f - g)(x)$[/tex] involves subtracting [tex]\(g(x)\)[/tex] from [tex]\(f(x)\)[/tex]:
[tex]\[
(f - g)(x) = f(x) - g(x)
\][/tex]
Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[
(f - g)(x) = (6x - 8) - (-5x + 2)
\][/tex]
Now, simplify the expression by distributing the negative sign inside the parenthesis:
[tex]\[
(f - g)(x) = 6x - 8 + 5x - 2
\][/tex]
Combine like terms to simplify further:
[tex]\[
(f - g)(x) = (6x + 5x) - (8 + 2)
\][/tex]
This gives us:
[tex]\[
(f - g)(x) = 11x - 10
\][/tex]
Thus, the simplified form of [tex]$(f - g)(x)$[/tex] is [tex]\(11x - 10\)[/tex].
Hence, the correct answer is:
[tex]\[
\boxed{11x - 10}
\][/tex]
