Choose the one alternative that best completes the statement or answers the question.
Find the domain of the rational function.
-$$h ( x ) = \frac { x + 5 } { x ^ { 2 } - 36 }$$
A) $\{ x \mid x \neq 0,36 \}$
B) $\{ x \mid x \neq - 6,6 , - 5 \}$
C) $\{ x \mid x \neq - 6,6 \}$
D) all real numbers

Question

Quizplus · Accepted Answer

The domain of a rational function includes all real numbers except those that make the denominator equal to zero. For $h(x) = \frac{x + 5}{x^2 - 36}$, the denominator is $x^2 - 36$, which factors to $(x - 6)(x + 6)$. Thus, the function is undefined when $x = 6$ or $x = -6$, making the correct domain $\{ x \mid x \neq - 6,6 \}$.

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