Question

given that $f(x) = x^2 + 5x + 6$ and $g(x) = x + 2$, find $(f + g)(x)$ and express the result as a polynomial in simplest form.

answer
attempt 1 out of 2

Explanation:

Step1: Recall the definition of function addition

The sum of two functions \( (f + g)(x) \) is defined as \( f(x) + g(x) \). So we need to add the two given functions \( f(x) = x^2 + 5x + 6 \) and \( g(x)=x + 2 \).

Step2: Add the functions

Substitute the expressions for \( f(x) \) and \( g(x) \) into the sum:
\( (f + g)(x)=f(x)+g(x)=(x^2 + 5x + 6)+(x + 2) \)
Now, combine like terms. The \( x^2 \) term has no like terms, so we keep it as is. For the \( x \) terms: \( 5x+x = 6x \). For the constant terms: \( 6 + 2=8 \).
So, \( (f + g)(x)=x^2+6x + 8 \).

Answer:

\( x^2 + 6x + 8 \)