Find $a$, such that the function $f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }$ has the domain $( - 4,4 )$.
A) $a = - 16$
B) $a = \sqrt { 4 }$
C) $a = - \sqrt { 4 }$
D) $a = 16$
E) $a = 4$

Question

Quizplus · Accepted Answer

The domain of the function is determined by the condition under the square root: $a - x^2 \geq 0$. For the domain $(-4, 4)$, $a$ must be such that $a - x^2 \geq 0$ for $-4 < x < 4$. This implies $a \geq 16$, and since the domain is open at $-4$ and $4$, $a = 16$ is the correct choice.

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Find $a$ , Such That the Function $f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }$