To solve these problems, we need to understand the properties of inverse functions. By definition, if [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are inverse functions, then for any value of [tex]\( x \)[/tex]:
[tex]\[ (h \circ k)(x) = x \][/tex]
and
[tex]\[ (k \circ h)(x) = x \][/tex]
This means that when we compose [tex]\( h \)[/tex] and [tex]\( k \)[/tex], or compose [tex]\( k \)[/tex] and [tex]\( h \)[/tex], we should get the input value back.
1. For the first part, [tex]\( (h \circ k)(3) \)[/tex]:
Since [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are inverse functions, applying [tex]\( k \)[/tex] first and then [tex]\( h \)[/tex] should return the original input value. Therefore:
[tex]\[ (h \circ k)(3) = 3 \][/tex]
2. For the second part, [tex]\( (k \circ h)(-4b) \)[/tex]:
Again, since [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are inverse functions, applying [tex]\( h \)[/tex] first and then [tex]\( k \)[/tex] should return the original input value. Therefore:
[tex]\[ (k \circ h)(-4b) = -4b \][/tex]
So, the values are:
[tex]\[ (h \circ k)(3) = 3 \][/tex]
[tex]\[ (k \circ h)(-4b) = -4b \][/tex]
