### Home > APCALC > Chapter 1 > Lesson 1.3.2 > Problem1-114

1-114.

State the domain of each of the following functions.

1. $f(x) =\sqrt { 25 - x ^ { 2 } }$

You should recognize that $f(x)$ is the equation of a semi-circle with radius $5$ and center at the origin.

2. $g(x) = \log(x + 5)$

The parent function, $y = \log x$, has an open domain of $0 < x > ∞$.

3. $h(x) =\frac { 5 x } { x ^ { 2 } - x - 12 }$

Factor the denominator. Remember, that the domain cannot support zeros in the denominator.

4. $k(x) =\frac { \sqrt { x + 2 } } { x ^ { 2 } - 4 }$

The numerator and denominator will be restricted in different ways. Combine both restrictions.

Domain: $x > −2$, $x ≠ 2$