To determine [tex]\((f - g)(x)\)[/tex] given the functions [tex]\(f(x) = 4^x - 8\)[/tex] and [tex]\(g(x) = 5x + 6\)[/tex], we need to perform the following steps:
1. Substitute the given expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into [tex]\((f - g)(x)\)[/tex]:
[tex]\[
(f - g)(x) = f(x) - g(x)
\][/tex]
2. Substitute [tex]\(f(x) = 4^x - 8\)[/tex] and [tex]\(g(x) = 5x + 6\)[/tex] into the equation:
[tex]\[
(f - g)(x) = (4^x - 8) - (5x + 6)
\][/tex]
3. Simplify the expression by distributing the negative sign and combining like terms:
[tex]\[
(f - g)(x) = 4^x - 8 - 5x - 6
\][/tex]
4. Combine the constants [tex]\(-8\)[/tex] and [tex]\(-6\)[/tex]:
[tex]\[
(f - g)(x) = 4^x - 5x - 14
\][/tex]
Therefore, the simplified form of [tex]\((f - g)(x)\)[/tex] is:
[tex]\[
(f - g)(x) = 4^x - 5x - 14
\][/tex]
Thus, the correct answer is:
D. [tex]\((f - g)(x) = 4^x - 5x - 14\)[/tex]
