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3.4.3 Quiz: Adding and Subtracting Functions

Question 8 of 10

If [tex]f(x) = 3x - 1[/tex] and [tex]g(x) = x + 2[/tex], find [tex](f - g)(x)[/tex].

A. [tex]4x + 1[/tex]

Sagot :

GinnyAnsweridn
To find [tex]\((f - g)(x)\)[/tex] when given the functions [tex]\( f(x) = 3x - 1 \)[/tex] and [tex]\( g(x) = x + 2 \)[/tex], let's follow these steps:

1. Write down the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ f(x) = 3x - 1 \][/tex]
[tex]\[ g(x) = x + 2 \][/tex]

2. To find [tex]\((f - g)(x)\)[/tex], subtract [tex]\( g(x) \)[/tex] from [tex]\( f(x) \)[/tex]:
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]

3. Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into the equation:
[tex]\[ (f - g)(x) = (3x - 1) - (x + 2) \][/tex]

4. Distribute the negative sign and combine like terms:
[tex]\[ (f - g)(x) = 3x - 1 - x - 2 \][/tex]
[tex]\[ (f - g)(x) = 3x - x - 1 - 2 \][/tex]
[tex]\[ (f - g)(x) = 2x - 3 \][/tex]

So, [tex]\((f - g)(x) = 2x - 3\)[/tex].

Therefore, none of the given choices (including "4x + 1") are the correct expression for [tex]\((f - g)(x)\)[/tex]. The correct answer should be:

[tex]\[ (f - g)(x) = 2x - 3 \][/tex]
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