What is $$ (f+g)(x) $$ ? $$ \begin{array}{l}f(x)=2 x+5 \ g(x)=x^{2}+5 x+4 \ \text { Write your answer as a polynomial or a rational }\end{array} $$

Question

UpStudy AI · Accepted Answer

To find $$(f+g)(x)$$, we add the functions $$f(x)$$ and $$g(x)$$ together.

1. Write the expressions for $$f(x)$$ and $$g(x)$$:
   $$
   f(x) = 2x + 5
   $$
   $$
   g(x) = x^2 + 5x + 4
   $$

2. Add $$f(x)$$ and $$g(x)$$:
   $$
   (f+g)(x) = f(x) + g(x) = (2x + 5) + (x^2 + 5x + 4)
   $$

3. Combine like terms:
   $$
   (f+g)(x) = x^2 + (2x + 5x) + (5 + 4) = x^2 + 7x + 9
   $$

Thus, the answer is:
$$
(f+g)(x) = x^2 + 7x + 9
$$
$$(f+g)(x) = x^2 + 7x + 9$$

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