### Home > APCALC > Chapter 1 > Lesson 1.5.1 > Problem1-202

1-202.

State the domain of each of the following functions.

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

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

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

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

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

$D = (−∞, ∞)$

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

$x^² - x - 6 ≠ 0$

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

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