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TIFR-2018-Maths-A: 13

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True/False Question :

Let $V$ be the vector space over $\mathbb{R}$ consisting of polynomials of degree less than or equal to $3$. Let $T:V \rightarrow V$ be the operator sending $f\left(t\right)$ to $f\left(t+1 \right)$, and $D:V \rightarrow V$ the operator sending $f\left(t \right)$ to $df\left(t \right)/dt$. Then $T$ is a polynomial in $D$.

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