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Question 12 of 25

If [tex]\( f(x) = 3^x + 10 \)[/tex] and [tex]\( g(x) = 2x - 4 \)[/tex], find [tex]\((f+g)(x)\)[/tex].

A. [tex]\( (f+g)(x) = 3^x + 2x + 6 \)[/tex]

B. [tex]\( (f+g)(x) = -3^x - 2x - 14 \)[/tex]

C. [tex]\( (f+g)(x) = 3^x - 2x + 14 \)[/tex]

D. [tex]\( (f+g)(x) = 5x + 6 \)[/tex]

Sagot :

GinnyAnswer
To find [tex]\((f+g)(x)\)[/tex] given the functions [tex]\(f(x) = 3^x + 10\)[/tex] and [tex]\(g(x) = 2x - 4\)[/tex], we need to add these functions together. Let's proceed with the step-by-step solution.

Step 1: Write down the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].

[tex]\[ f(x) = 3^x + 10 \][/tex]
[tex]\[ g(x) = 2x - 4 \][/tex]

Step 2: Add [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] to find [tex]\((f+g)(x)\)[/tex].

[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]

Step 3: Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].

[tex]\[ (f+g)(x) = (3^x + 10) + (2x - 4) \][/tex]

Step 4: Combine like terms.

[tex]\[ (f+g)(x) = 3^x + 10 + 2x - 4 \][/tex]

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

Therefore, the function [tex]\((f+g)(x)\)[/tex] simplifies to:

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

So, the correct answer is:

A. [tex]\((f+g)(x) = 3^x + 2x + 6\)[/tex].
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