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L 24.3 Quiz: Combining Functions

Question 2 of 10

Given:
[tex]\[
\begin{array}{l}
f(x) = |2x + 3| - 5 \\
g(x) = 7
\end{array}
\][/tex]

Find [tex]\((f - g)(x)\)[/tex].

A. [tex]\((f - g)(x) = |2x| - 9\)[/tex]

B. [tex]\((f - g)(x) = |2x - 2| - 7\)[/tex]

C. [tex]\((f - g)(x) = |2x - 9|\)[/tex]

D. [tex]\((f - g)(x) = |2x + 3| - 12\)[/tex]

Sagot :

GinnyAnswer
To solve the problem of finding [tex]\((f - g)(x)\)[/tex] given the functions [tex]\( f(x) = |2x + 3| - 5 \)[/tex] and [tex]\( g(x) = 7 \)[/tex], let's break down the steps:

1. Understand the Definition of the Function [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:

- [tex]\( f(x) = |2x + 3| - 5 \)[/tex]
- [tex]\( g(x) = 7 \)[/tex]

2. Determine what [tex]\((f - g)(x)\)[/tex] Means:

[tex]\((f - g)(x)\)[/tex] means we subtract [tex]\(g(x)\)[/tex] from [tex]\(f(x)\)[/tex]:
[tex]\[ (f - g)(x) = f(x) - g(x) \][/tex]

3. Substitute the Functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] into the Expression:

We need to substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ (f - g)(x) = (|2x + 3| - 5) - 7 \][/tex]

4. Simplify the Expression:

Combine the constants:
[tex]\[ (f - g)(x) = |2x + 3| - 5 - 7 \][/tex]
[tex]\[ (f - g)(x) = |2x + 3| - 12 \][/tex]

So, the correct solution is:
[tex]\[ (f - g)(x) = |2x + 3| - 12 \][/tex]

Thus, the correct answer is:
[tex]\[ \boxed{D. (f - g)(x) = |2 x + 3| - 12} \][/tex]
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