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If [tex]$f(x)=3^x+10x$[/tex] and [tex]$g(x)=5x-3$[/tex], find [tex][tex]$(f+g)(x)$[/tex][/tex].

A. [tex]$18x-3$[/tex]

B. [tex]$3^x+5x+3$[/tex]

C. [tex][tex]$3^x+15x-3$[/tex][/tex]

D. [tex]$3^x-5x+3$[/tex]

Sagot :

GinnyAnswer
To determine [tex]\((f+g)(x)\)[/tex], we need to add the given functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].

Given:
[tex]\[ f(x) = 3^x + 10x \][/tex]
[tex]\[ g(x) = 5x - 3 \][/tex]

The function [tex]\((f+g)(x)\)[/tex] is found by adding the two functions together:
[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]

Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into the equation:
[tex]\[ (f+g)(x) = (3^x + 10x) + (5x - 3) \][/tex]

Now, combine like terms:
[tex]\[ (f+g)(x) = 3^x + 10x + 5x - 3 \][/tex]
[tex]\[ (f+g)(x) = 3^x + 15x - 3 \][/tex]

Thus, the correct expression for [tex]\((f+g)(x)\)[/tex] is:
[tex]\[ (f+g)(x) = 3^x + 15x - 3 \][/tex]

Therefore, the correct answer is:
C. [tex]\(3^x + 15x - 3\)[/tex]
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