CPM Homework Help : CALC Problem 1-114

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1-114.

State the domain for each of the following functions.

$f ( x ) = \sqrt { 25 - x ^ { 2 } }$
Hint (a):
You should recognize that $f(x)$ is the equation of a semi-circle with radius $5$ and center at the origin.

$g ( x ) = \operatorname { log } ( x + 5 )$
Hint (b):
The parent function, $y =\operatorname{log}x$ , has an open domain of $0 < x > ∞$ .

$h ( x ) = \frac { 5 x } { x ^ { 2 } - x - 12 }$
Hint (c):
Factor the denominator. Remember, that the domain cannot support zeros in the denominator.

$k ( x ) = \frac { \sqrt { x + 2 } } { x ^ { 2 } - 4 }$
Hint (d):
The numerator and denominator will be restricted in different ways. Combine both restrictions.
Answer (d):
Domain: $x > -2$ , $x ≠ 2$

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