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Let [tex]$f(x) = 3 + 8x$[/tex] and [tex]$g(x) = 5x - 2$[/tex].

Find [tex][tex]$(f + g)(x)$[/tex][/tex].

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

Sagot :

GinnyAnswer
Sure, let's find the combined function [tex]\((f+g)(x)\)[/tex] given the functions [tex]\(f(x) = 3 + 8x\)[/tex] and [tex]\(g(x) = 5x - 2\)[/tex].

We need to add these two functions together to find [tex]\((f+g)(x)\)[/tex].

Step by step:

1. Start by writing down the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ f(x) = 3 + 8x \][/tex]
[tex]\[ g(x) = 5x - 2 \][/tex]

2. Now add [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ (f+g)(x) = f(x) + g(x) \][/tex]
Substitute the expressions of [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] into the equation:
[tex]\[ (f+g)(x) = (3 + 8x) + (5x - 2) \][/tex]

3. Combine the like terms:
[tex]\[ (f+g)(x) = 3 + 8x + 5x - 2 \][/tex]

4. Combine the constants and the terms involving [tex]\(x\)[/tex]:
[tex]\[ (f+g)(x) = (3 - 2) + (8x + 5x) \][/tex]
Simplify the constants and the coefficients of [tex]\(x\)[/tex]:
[tex]\[ (f+g)(x) = 1 + 13x \][/tex]

Thus, the combined function:

[tex]\((f+g)(x) = 1 + 13x\)[/tex]
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