(a) Show that if f and g are functions for whichf(x) = g(x) and g(x) = f(x)for all x

Chapter 4, Problem 35

(choose chapter or problem)

(a) Show that if f and g are functions for which

$f^{\prime}(x)=g(x) \text { and } g^{\prime}(x)=-f(x)$

for all x, then $f^{2}(x)+g^{2}(x)$ is a constant.

(b) Give an example of functions f and g with this property.

Equation Transcription:

${f}^{'}(x)=g(x)\ and \ {g}^{'}(x)=-f(x)$

${f}^{2}(x)+{g}^{2}(x)$

Text Transcription:

f'(x)=g(x) and g'(x)=-f(x)

f^2(x)+g^2(x)

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