Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Our platform provides a seamless experience for finding precise answers from a network of experienced professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To find the inverse of a function at a specific point, we need to understand the relationship between the function [tex]\( f \)[/tex] and its inverse [tex]\( f^{-1} \)[/tex].
Given that [tex]\( f(-3) = 6 \)[/tex], this means that when we input [tex]\(-3\)[/tex] into the function [tex]\( f \)[/tex], the output is [tex]\( 6 \)[/tex]. The purpose of finding the inverse function [tex]\( f^{-1}(x) \)[/tex] is to determine what input into [tex]\( f \)[/tex] would yield a given output [tex]\( x \)[/tex].
In this case, since [tex]\( f(a) = b \)[/tex] implies [tex]\( f^{-1}(b) = a \)[/tex], we know that if [tex]\( f(-3) = 6 \)[/tex], then [tex]\( f^{-1}(6) \)[/tex] must be [tex]\(-3\)[/tex].
Therefore, [tex]\( f^{-1}(6) = -3 \)[/tex].
So, we fill in the blank as follows:
If a function [tex]\( f \)[/tex] has an inverse and [tex]\( f(-3)=6 \)[/tex], then [tex]\( f^{-1}(6) = \boxed{-3} \)[/tex].
Given that [tex]\( f(-3) = 6 \)[/tex], this means that when we input [tex]\(-3\)[/tex] into the function [tex]\( f \)[/tex], the output is [tex]\( 6 \)[/tex]. The purpose of finding the inverse function [tex]\( f^{-1}(x) \)[/tex] is to determine what input into [tex]\( f \)[/tex] would yield a given output [tex]\( x \)[/tex].
In this case, since [tex]\( f(a) = b \)[/tex] implies [tex]\( f^{-1}(b) = a \)[/tex], we know that if [tex]\( f(-3) = 6 \)[/tex], then [tex]\( f^{-1}(6) \)[/tex] must be [tex]\(-3\)[/tex].
Therefore, [tex]\( f^{-1}(6) = -3 \)[/tex].
So, we fill in the blank as follows:
If a function [tex]\( f \)[/tex] has an inverse and [tex]\( f(-3)=6 \)[/tex], then [tex]\( f^{-1}(6) = \boxed{-3} \)[/tex].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.