Given that functions [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are inverse functions, we have the following properties:
1. [tex]\( h \circ k \)[/tex] means [tex]\( h \)[/tex] composed with [tex]\( k \)[/tex], or [tex]\( h(k(x)) = x \)[/tex].
2. [tex]\( k \circ h \)[/tex] means [tex]\( k \)[/tex] composed with [tex]\( h \)[/tex], or [tex]\( k(h(x)) = x \)[/tex].
For the given compositions:
1. [tex]\( (h \circ k)(3) = h(k(3)) \)[/tex].
Since [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are inverse functions, [tex]\( h(k(3)) = 3 \)[/tex].
So, [tex]\( (h \circ k)(3) = 3 \)[/tex].
2. [tex]\( (k \circ h)(-4b) = k(h(-4b)) \)[/tex].
Again, because [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are inverse functions, [tex]\( k(h(-4b)) = -4b \)[/tex].
Thus, [tex]\( (k \circ h)(-4b) = -16 \)[/tex].
Filling in the blanks, we get:
[tex]\[
\begin{array}{l}
(h \circ k)(3) = 3 \\
(k \circ h)(-4b) = 16 \\
\end{array}
\][/tex]
