Let f: Z → Z be defined as f(x)= >= { x + 9 √x+9 x-7 Find a formula for f-1. if x is odd if x is even
Let f: Z → Z be defined as f(x)= >= { x + 9 √x+9 x-7 Find a formula for f-1. if x is odd if x is even
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
find the formula
![Let \( f: \mathbb{Z} \to \mathbb{Z} \) be defined as
\[
f(x) =
\begin{cases}
x + 9 & \text{if } x \text{ is odd} \\
x - 7 & \text{if } x \text{ is even}
\end{cases}
\]
Find a formula for \( f^{-1} \).
\[
f^{-1}(x) =
\begin{cases}
\text{(box to input formula)} & \text{if } x \text{ is even} \\
\text{(box to input formula)} & \text{if } x \text{ is odd}
\end{cases}
\]
There is a visual indication that the inputs for the inverse function are incorrect, as shown by red crosses next to the input boxes.
There is also an "eBook" button at the bottom, presumably for accessing additional resources or information.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc5cb102b-2da8-445c-8120-9910543aeab8%2F2c05ad51-6f72-42f8-b32d-843e5ba892aa%2F9ezz8at_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( f: \mathbb{Z} \to \mathbb{Z} \) be defined as
\[
f(x) =
\begin{cases}
x + 9 & \text{if } x \text{ is odd} \\
x - 7 & \text{if } x \text{ is even}
\end{cases}
\]
Find a formula for \( f^{-1} \).
\[
f^{-1}(x) =
\begin{cases}
\text{(box to input formula)} & \text{if } x \text{ is even} \\
\text{(box to input formula)} & \text{if } x \text{ is odd}
\end{cases}
\]
There is a visual indication that the inputs for the inverse function are incorrect, as shown by red crosses next to the input boxes.
There is also an "eBook" button at the bottom, presumably for accessing additional resources or information.
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