To solve for [tex]\((f-g)(x)\)[/tex], we need to determine the expression that results by subtracting the function [tex]\(g(x)\)[/tex] from the function [tex]\(f(x)\)[/tex].
Given:
[tex]\[ f(x) = 4^x - 8 \][/tex]
[tex]\[ g(x) = 5x + 6 \][/tex]
We want to find [tex]\( (f-g)(x) \)[/tex]:
[tex]\[
(f-g)(x) = f(x) - g(x)
\][/tex]
Substituting the given functions into the equation:
[tex]\[
(f-g)(x) = (4^x - 8) - (5x + 6)
\][/tex]
Now, distribute the negative sign through the second term:
[tex]\[
(f-g)(x) = 4^x - 8 - 5x - 6
\][/tex]
Combine like terms:
[tex]\[
(f-g)(x) = 4^x - 5x - 14
\][/tex]
Thus, the simplified form of [tex]\((f-g)(x)\)[/tex] is:
[tex]\[
(f-g)(x) = 4^x - 5x - 14
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{A. (f-g)(x) = 4^x - 5x - 14}
\][/tex]
