Show that if a function ƒ is defined on an interval
Chapter 7, Problem 75E(choose chapter or problem)
Show that if a function \(f\) is defined on an interval symmetric about the origin (so that \(f\) is defined at \(−x\) whenever it is defined at \(x\)), then
\(f(x)=\frac{f(x)+f(-x)}{2}+\frac{f(x)-f(-x)}{2}\)
Then show that \((f(x)+f(-x)) / 2\) is even and that \((f(x)-f(-x)) / 2\) is odd.
Equation Transcription:
Text Transcription:
f
-x
x
f(x) = f(x) + f(-x) / 2 + f(x)-f(-x)/ 2
(f(x) + f(-x))/2
(f(x) - f(-x))/2
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