x, if -1くx<
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
Refer to the following piecewise function.
f(-2) =
f(0) =
f(1) =
![The image represents a piecewise function \( f(x) \), which is defined as follows:
\[
f(x) =
\begin{cases}
1, & \text{if } x \leq -1 \\
x, & \text{if } -1 < x < 0 \\
2 - x, & \text{if } x \geq 0
\end{cases}
\]
This function specifies different expressions for \( f(x) \) depending on the interval in which the variable \( x \) falls:
1. For \( x \leq -1 \), the function \( f(x) \) is constant and equal to 1.
2. For \( -1 < x < 0 \), the function \( f(x) \) is linear and equal to \( x \).
3. For \( x \geq 0 \), the function \( f(x) \) is defined as \( 2 - x \), which is a linear function with a negative slope.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37572b38-2702-41fa-bc8c-966854898153%2F46dcb9f9-20b8-47c0-a344-0a2878531f84%2F3sv2w2r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image represents a piecewise function \( f(x) \), which is defined as follows:
\[
f(x) =
\begin{cases}
1, & \text{if } x \leq -1 \\
x, & \text{if } -1 < x < 0 \\
2 - x, & \text{if } x \geq 0
\end{cases}
\]
This function specifies different expressions for \( f(x) \) depending on the interval in which the variable \( x \) falls:
1. For \( x \leq -1 \), the function \( f(x) \) is constant and equal to 1.
2. For \( -1 < x < 0 \), the function \( f(x) \) is linear and equal to \( x \).
3. For \( x \geq 0 \), the function \( f(x) \) is defined as \( 2 - x \), which is a linear function with a negative slope.
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