Question
For the piecewise function \( f(x)=\left\{\begin{array}{ll}4-x & \text { for } x \leq 2 \\ 2 x+1 & \text { for } x>2\end{array}\right. \) find \( f(0) \) \( \square \) A
Ask by Macdonald Pope. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(0) = 4 \)
Solution
1. Since \( f(x) \) is given as a piecewise function, for \( x \leq 2 \) the function is defined as
\[
f(x) = 4 - x.
\]
2. For \( x = 0 \), because \( 0 \leq 2 \), we use the first piece:
\[
f(0) = 4 - 0 = 4.
\]
3. Therefore,
\[
f(0) = 4.
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find \( f(0) \), we first identify which part of the piecewise function to use. Since \( 0 \leq 2 \), we use the first part of the function: \( f(x) = 4 - x \). Plugging in \( 0 \) gives us \( f(0) = 4 - 0 = 4 \). Thus, \( f(0) \) is \( 4 \). Another interesting aspect is that piecewise functions often represent real-world situations, such as a company's pricing strategy based on quantity, or tax brackets. These functions allow us to model systems where different rules apply under different conditions, making them both practical and fun to analyze!
