To find [tex]\( (f-g)(x) \)[/tex], we need to subtract the function [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex].
Given:
[tex]\[ f(x) = 4^x - 8 \][/tex]
[tex]\[ g(x) = 5x + 6 \][/tex]
Now, let's perform the subtraction step-by-step:
[tex]\[ (f-g)(x) = f(x) - g(x) \][/tex]
[tex]\[ (f-g)(x) = (4^x - 8) - (5x + 6) \][/tex]
Distribute the minus sign within the parentheses:
[tex]\[ (f-g)(x) = 4^x - 8 - 5x - 6 \][/tex]
Combine like terms:
[tex]\[ (f-g)(x) = 4^x - 5x - 8 - 6 \][/tex]
[tex]\[ (f-g)(x) = 4^x - 5x - 14 \][/tex]
Thus, the function [tex]\( (f-g)(x) \)[/tex] simplifies to:
[tex]\[ (f-g)(x) = 4^x - 5x - 14 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{4^x - 5x - 14} \][/tex]
So the correct choice from the given options is:
D. [tex]\((f-g)(x) = 4^x - 5x - 14\)[/tex]
