Write the domain in interval notation. (a) \( a(x)=\sqrt{x+16} \) (b) \( b(x)=\sqrt{16-x} \) (c) \( c(x)=\frac{1}{\sqrt{x+16}} \)

For the function \( a(x)=\sqrt{x+16} \), the expression inside the square root must be non-negative. This means \( x + 16 \geq 0 \), which simplifies to \( x \geq -16 \). In interval notation, the domain is \( [-16, \infty) \). For the function \( b(x)=\sqrt{16-x} \), the expression under the square root must also be non-negative. Thus, \( 16 - x \geq 0 \) leads to \( x \leq 16 \). Therefore, in interval notation, the domain is \( (-\infty, 16] \). For the function \( c(x)=\frac{1}{\sqrt{x+16}} \), the square root in the denominator must be positive, meaning \( x + 16 > 0 \), which simplifies to \( x > -16 \). The domain in interval notation is \( (-16, \infty) \).