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Question 2 (Multiple Choice Worth 4 points)
(Exponential Functions and Function Combinations MC)

Given [tex]f(x) = 6x - 8[/tex] and [tex]g(x) = -5x + 2[/tex], what is [tex](f - g)(x)[/tex]?

A. [tex]x - 10[/tex]
B. [tex]x - 6[/tex]
C. [tex]11x - 10[/tex]
D. [tex]11x - 6[/tex]

Sagot :

GinnyAnsweridn
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]
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