Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

An increasing function f satisfies f(10) = 5 and f'(10) = 8. Which of the following statements about the
inverse of f must be true?

(A). (f^-1)’(5) = 10
(B). (f^-1)’(8) = 10
(C). (f^-1)’(5) = 8
(D). (f^-1)’(5) = 1/8

Sagot :

Answer:  D

Explanation:

Because [tex]f^{-1}'(y)=\frac{1}{f'(x)}[/tex] and y=5 when x=10, [tex]f^{-1}'(5)=\frac{1}{f'(10)}=\frac{1}{8}[/tex]

MrRoyal

The given equations are illustrations of inverse functions. The statement about the inverse of f that must be true is: [tex]f^{-1}(5) = \frac{1}{8}[/tex]

Given that:

[tex]f(10) = 5[/tex]

[tex]f'(10) = 8[/tex]

[tex]f(10) = 5[/tex] means that:

[tex]x = 10[/tex] and [tex]y = 5[/tex]

So, the relationship between the inverse of both functions is:

[tex]f^{-1}(y) = \frac{1}{f^{-1}(x)}[/tex]

Substitute values for x and y

[tex]f^{-1}(5) = \frac{1}{f^{-1}(10)}[/tex]

Substitute [tex]f'(10) = 8[/tex]

[tex]f^{-1}(5) = \frac{1}{8}[/tex]

Hence, option D is true, i.e.

[tex]D.\ f^{-1}(5) = \frac{1}{8}[/tex]

Read more about inverse functions at:

https://brainly.com/question/10300045

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.