Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Functions [tex]\( h \)[/tex] and [tex]\( k \)[/tex] are inverse functions and are defined for all real numbers. Determine the value of each function composition.

[tex]\[
\begin{array}{l}
(h \circ k)(3) = \square \\
(k \circ h)(-4b) = \square
\end{array}
\][/tex]

Sagot :

GinnyAnswer
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]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.