andreyram25
Answered

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Question 2 of 25

If [tex]f(x) = 2x - 6[/tex] and [tex]g(x) = 3x + 9[/tex], find [tex](f + g)(x)[/tex].

A. [tex](f + g)(x) = 5x + 3[/tex]
B. [tex](f + g)(x) = -x - 15[/tex]
C. [tex](f + g)(x) = x + 15[/tex]
D. [tex](f + g)(x) = 5x + 15[/tex]

Sagot :

GinnyAnswer
To find \((f + g)(x)\), we need to add the functions \(f(x)\) and \(g(x)\).

Given:
[tex]\[ f(x) = 2x - 6 \][/tex]
[tex]\[ g(x) = 3x + 9 \][/tex]

Let's add \(f(x)\) and \(g(x)\):

[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]
[tex]\[ (f + g)(x) = (2x - 6) + (3x + 9) \][/tex]

Combine the like terms:

[tex]\[ (f + g)(x) = 2x + 3x - 6 + 9 \][/tex]
[tex]\[ (f + g)(x) = 5x + 3 \][/tex]

Upon examining the given options:

A. \((f + g)(x) = 5x + 3\)
B. \((f + g)(x) = -x - 15\)
C. \((f + g)(x) = x + 15\)
D. \((f + g)(x) = 5x + 15\)

The correct answer is:
[tex]\[ A. (f + g)(x) = 5x + 3 \][/tex]
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