If [tex]f(x)=\left\{\begin{array}{cc}x^2+2 & x \ \textless \ 1 \\ x-3 & x \ \textgreater \ 1\end{array}\right.[/tex] then find [tex]f(1)[/tex] if exist [tex]=[/tex] does nt exist
Answer (2)
The function f ( x ) is defined piecewise for x < 1 and 1"> x > 1 .
The function is not defined at x = 1 .
Therefore, f ( 1 ) does not exist. does nt exist
Explanation
Analysis of the problem We are given a piecewise function f ( x ) and asked to determine if f ( 1 ) exists. The function is defined as:
1\end{array}\right."> f ( x ) = { x 2 + 2 x − 3 x < 1 x > 1
Notice that the function is defined for x < 1 and 1"> x > 1 , but there is no definition for x = 1 .
Determining if f(1) exists Since the function f ( x ) is not defined at x = 1 , we can conclude that f ( 1 ) does not exist.
Final Answer Therefore, f ( 1 ) does not exist.
Examples
In electrical engineering, piecewise functions can model the voltage or current in a circuit that changes abruptly at certain times. For example, a voltage source might output a constant voltage until a switch is flipped, at which point the voltage changes to a different value. Understanding how to evaluate and analyze such functions is crucial for designing and troubleshooting electrical systems.
The function f ( x ) is not defined at x = 1 as it only gives expressions for values less than and greater than 1. Consequently, f ( 1 ) does not exist. Thus, we conclude that f ( 1 ) = does not exist .
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