State the domain of each of the following functions.

1. $f(x) = \sec(x)$

   Hint (a):

   $\text{sec}(x)=\frac{1}{\text{cos}(x)}$

   More Help (a):

   When is the $\cos(x) = 0$?

2. $g(x) = \log(x^2 + 1)$

   Hint (b):

   Logarithms have restrictive domains: $x$ cannot be less than or equal to $0$. What value(s) of $x$ will make $x^² + 1 ≤ 0$?

   Answer (b):

   $D = (−∞, ∞)$

3. $h(x) =\frac { x ^ { 2 } - 4 } { x ^ { 2 } - x - 6 }$

   Hint (c):

   $x^² - x - 6 ≠ 0$

4. $k ( x ) = \frac { \operatorname { log } ( x - 1 ) } { \sqrt { x ^ { 2 } - 16 } }$

   Hint (d):

   Both the numerator and the denominator have restricted domains. To find the domain of $k(x)$, all restrictions apply... combine the domains together.