Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

Refer to the following piecewise function.

f(-2) = 
f(0) = 
f(1) = 

The image shows a piecewise function \( f(x) \) defined as follows: \[ f(x) = \begin{cases} x^2 + 2x + 1, & \text{if } x \leq -2 \\ 1 - x^2, & \text{if } x > -2 \end{cases} \] This function has two different expressions based on the value of \( x \). - For values of \( x \) less than or equal to -2, the function is defined by the quadratic expression \( x^2 + 2x + 1 \). - For values of \( x \) greater than -2, the function is defined by the expression \( 1 - x^2 \). The function evaluates differently depending on which interval the input \( x \) belongs to.
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Transcribed Image Text:The image shows a piecewise function \( f(x) \) defined as follows: \[ f(x) = \begin{cases} x^2 + 2x + 1, & \text{if } x \leq -2 \\ 1 - x^2, & \text{if } x > -2 \end{cases} \] This function has two different expressions based on the value of \( x \). - For values of \( x \) less than or equal to -2, the function is defined by the quadratic expression \( x^2 + 2x + 1 \). - For values of \( x \) greater than -2, the function is defined by the expression \( 1 - x^2 \). The function evaluates differently depending on which interval the input \( x \) belongs to.
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