(Solution) - a Show that if f f x then the -(2025 Original AI-Free Solution)

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(a) Show that if f = f (x), then the function D: C2(-?, ?) ? F(-?, ?) defined by D(f) = f?? (x) is a linear transformation.
(b) Find a basis for the kernel of D.
(c) Show that the functions satisfying the equation D(f) = f(x) form a two-dimensional subspace of C2(-?, ?), and find a basis for this subspace.