Consider the function: f(x)=(x+1)/(x+2) (a) Find the domain of f.

To find the domain of the function \( f(x) = \frac{x+1}{x+2} \), we need to determine the values of \( x \) for which the function is defined. The function is a rational function, and it is defined for all real numbers except where the denominator is zero.<br /><br />The denominator of the function is \( x + 2 \). We set the denominator equal to zero to find the values of \( x \) that are not in the domain:<br /><br />\[ x + 2 = 0 \]<br /><br />Solving for \( x \):<br /><br />\[ x = -2 \]<br /><br />Therefore, the function \( f(x) = \frac{x+1}{x+2} \) is undefined at \( x = -2 \).<br /><br />The domain of \( f \) is all real numbers except \( x = -2 \). In interval notation, the domain is:<br /><br />\[ (-\infty, -2) \cup (-2, \infty) \]<br /><br />So, the domain of \( f \) is:<br /><br />\[ \boxed{(-\infty, -2) \cup (-2, \infty)} \]