Enter the subfunction $(f(x) \Rightarrow)$ and subdomain for $a$ in order and separated by a comma. (Example: $|x+3|-7, x<2$ ) Enter the subdomain as a single equality or inequality.
$-x+2,0<=x<=2$
Enter the subfunction $(f(x)=)$ and subdomain for $b$ in order and separated.
Answer (2)
The problem defines a piecewise function.
The first subfunction is − x + 2 for 0 ≤ x ≤ 2 .
We need to define the next subfunction and its domain.
Assuming the user provides x + 1 for 2 < x ≤ 4 , the piecewise function is defined as shown above.
Explanation
Understanding the Problem We are given a piecewise function f ( x ) . The first part of the function is defined as − x + 2 for 0 ≤ x ≤ 2 . We need to define the next subfunction and its domain, which will be provided by the user.
Defining the Next Subfunction Let's assume the user provides the subfunction x + 1 and the domain 2 < x ≤ 4 . Then the piecewise function would be defined as: f ( x ) = { − x + 2 , x + 1 , 0 ≤ x ≤ 2 2 < x ≤ 4 We are waiting for the user to provide the next subfunction and its domain.
Examples
Piecewise functions are used in real life to model situations where different rules or conditions apply over different intervals. For example, the cost of electricity might be different based on the time of day, or the postage cost might vary based on the weight of the package. Understanding piecewise functions helps in analyzing and modeling such scenarios effectively.
The piecewise function has two parts: the first is defined as − x + 2 for 0 ≤ x ≤ 2 , and the second is x + 1 for 2 < x ≤ 4 . This allows us to apply different expressions depending on the value of x . Make sure to define your second subfunction based on your specific needs.
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