Find the range for the function f(x) = (x+4)/(x2+3x+2) with domain x R - \-2, -1\

Here are the ranges for the given functions:

a) For $f(x) = \frac{x+4}{x^2+3x+2}$ with domain $x \in \mathbb{R} - \{-2, -1\}$:

Step 1: Factor the denominator and set $y = f(x)$.

$$y = \frac{x+4}{(x+1)(x+2)}$$

Step 2: Rearrange the equation to form a quadratic in $x$ in terms of $y$.

$$y(x^2+3x+2) = x+4$$ $$yx^2 + 3yx + 2y = x+4$$ $$$$