Question

1. given $f(x) = x^2 + 5x + 6$ and $g(x) = x + 2$, find: $(f + g)(x) = \square$ $(f - g)(x) = \square$

Explanation:

Step1: Find \((f + g)(x)\)

To find \((f + g)(x)\), we use the definition of function addition: \((f + g)(x)=f(x)+g(x)\). Substitute \(f(x)=x^{2}+5x + 6\) and \(g(x)=x + 2\) into the formula:

$$
LATEXBLOCK0
$$

Step2: Find \((f - g)(x)\)

To find \((f - g)(x)\), we use the definition of function subtraction: \((f - g)(x)=f(x)-g(x)\). Substitute \(f(x)=x^{2}+5x + 6\) and \(g(x)=x + 2\) into the formula:

$$
LATEXBLOCK1
$$

Answer:

\((f + g)(x)=\boldsymbol{x^{2}+6x + 8}\)
\((f - g)(x)=\boldsymbol{x^{2}+4x + 4}\)