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 $f(x) = 4x + \sqrt{a - x^2}$ is determined by the condition $a - x^2 \geq 0$, which ensures the expression under the square root is non-negative. Solving $a - x^2 \geq 0$ for $x$ gives $x^2 \leq a$. For the domain to be $(-4, 4)$, the maximum value of $x^2$ is $16$, when $x = 4$ or $x = -4$. Therefore, $a$ must be at least $16$, making $a = 16$ the correct choice to ensure the domain is $(-4, 4)$.

Find aaa , Such That the Function f(x)=4x+a−x2f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }f(x)=4x+a−x2​

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