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Which of the following are subspaces of the vector space of real-valued functions of a real...

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Basic Math

Which of the following are subspaces of the vector space ofreal-valued functions of a real variables? (must select all of thesubspaces.)

A. The set of even function (f(-x) = f(x) for all numbersx).

B. The set of odd functions (f(-x) = -f(x) for all real numbersx).

C. The set of functions f such that f(0) = 7

D. The set of functions f such that f(7) = 0

Answer & Explanation Solved by verified expert
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A Let S be the set of all even functions Now if and g are even functions then fgx fxgx fxgx fgx so that fg is an even function ie S is closed under vector addition Further if k is a scalar then kfx kfx kfx so that kf is an even function ie S is closed under scalar multiplication Also the zero function    See Answer
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