This builds on example given in class; Let C_R be the set of all real valued...

This builds on example given in class;

Let C_R be the set of all real valued continuous functions, and S_R be the subset of all symmetric real valued continuous functions.

We have verified that S_R has the zero Vector, and is closed under pointwise addition.

Show that the subset S_R is actually a Subspace by verifying the closure under scalar multiplication, namely,

if r is any real number,
and f is any Symmetric real valued function,
Show that the function (rf) is also a symmetric real valued continuous function.
Draw a graph to show f, rf and what makes the function (rf) symmetric.

Expert Solution

If some other explanation is needed then please write..

Thank you.

Colby Messinger answered 7 months ago

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