Let's analyze the given functions and fill out the table step-by-step for each of the inverse functions [tex]\( f(x) \)[/tex] and [tex]\( d(x) \)[/tex]:
1. For [tex]\( x = -8 \)[/tex]:
- Since [tex]\( x \leq 0 \)[/tex], we use the inverse function [tex]\( d(x) = -\sqrt{\frac{1}{2} x + 4} \)[/tex].
- We need to find [tex]\( d(-8) \)[/tex].
- According to the provided correct values, [tex]\( d(-8) = -0.0 \)[/tex].
2. For [tex]\( x = 0 \)[/tex]:
- Since [tex]\( x \geq 0 \)[/tex], we use the inverse function [tex]\( f(x) = \sqrt{\frac{1}{2} x + 4} \)[/tex].
- We need to find [tex]\( f(0) \)[/tex].
- According to the provided correct values, [tex]\( f(0) = 2.0 \)[/tex].
3. For [tex]\( x = 10 \)[/tex]:
- Since [tex]\( x \geq 0 \)[/tex], we use the inverse function [tex]\( f(x) = \sqrt{\frac{1}{2} x + 4} \)[/tex] for [tex]\( f \)[/tex].
- We also use the inverse function [tex]\( d(x) = -\sqrt{\frac{1}{2} x + 4} \)[/tex] for [tex]\( d \)[/tex].
- We need to find [tex]\( f(10) \)[/tex] and [tex]\( d(10) \)[/tex].
- According to the provided correct values, [tex]\( f(10) = 3.0 \)[/tex] and [tex]\( d(10) = -3.0 \)[/tex].
Hence, we can fill out the blanks in the table as follows:
[tex]\[
\begin{array}{l}
q = -0.0 \\
r = 2.0 \\
s = 3.0 \\
t = -3.0 \\
\end{array}
\][/tex]
