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If [tex]\( f(x) = 4^x - 8 \)[/tex] and [tex]\( g(x) = 5x + 6 \)[/tex], find [tex]\( (f - g)(x) \)[/tex].

A. [tex]\( (f - g)(x) = 4^x + 5x - 2 \)[/tex]

B. [tex]\( (f - g)(x) = -x - 14 \)[/tex]

C. [tex]\( (f - g)(x) = -4^x + 5x + 14 \)[/tex]

D. [tex]\( (f - g)(x) = 4^x - 5x - 14 \)[/tex]

Sagot :

GinnyAnswer
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]
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