Let and let be the function defined by.

Question

Let $W = [S]$ and let $T: V \to V$ be the function defined by

$\quad \quad T(f(x)) = \frac{d^2}{dx^2}(f(x)) + 2\frac{d}{dx}(f(x))$ .
$\quad$

09 Jan 2026

Answer :

Word Count : 111

Let (S={e^{-x},, x e^{-x}}) and let (W=[S]). Define (T:W\to W) by [ T(f)=\frac{d^{2}}{dx^{2}}(f)+2\frac{d}{dx}(f). ] First compute (T) on the basis elements. For ___ ________ __________ ___ __________.
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