QuestionWhat is $(f+g)(x)$ ? $\begin{array}{l} f(x)=-2 x^{2}-4 x \\ g(x)=3 x+1 \end{array}$
Write your answer as a polynomial or a rational function in simplest form.

Studdy Solution

STEP 1

1. We are given two functions, $f(x)$ and $g(x)$ .
2. We need to find the sum of these two functions, denoted as $(f+g)(x)$ .
3. The result should be expressed as a polynomial in its simplest form.

STEP 2

1. Write the expression for $(f+g)(x)$ .
2. Combine like terms to simplify the expression.

STEP 3

Write the expression for $(f+g)(x)$ by adding the functions $f(x)$ and $g(x)$ :
$(f+g)(x) = f(x) + g(x) = (-2x^2 - 4x) + (3x + 1)$

STEP 4

Combine like terms in the expression:
1. Combine the $x^2$ terms: $-2x^2$ .
2. Combine the $x$ terms: $-4x + 3x = -x$ .
3. Combine the constant terms: $1$ .
The simplified expression is:
$(f+g)(x) = -2x^2 - x + 1$
The polynomial in its simplest form is:
$\boxed{-2x^2 - x + 1}$

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