Question

Let $V$ be the real vector space consisting of all polynomials in one variable with real coefficients and having degree at most 6, together with the zero polynomial. Then which one of the following is true?

• A. $\\{ f \in V : f(1/2) € Q \\}$ is a subspace of $V$.
• B. $\\{ f \in V : f(1/2) = 1 \\}$ is a subspace of $V$.
• C. $\\{ f \in V : f(1/2) = f(1) \\}$ is a subspace of $V$.
• D. $\\{ f \in V : f'(1/2) = 1\\}$ is a subspace of $V$.

Answer 1

Answer: (C)

$\\{ f \in V : f(1/2) = f(1) \\}$ is a subspace of $V$.

Answer 2

The correct option is (C): $\\{ f \in V : f(1/2) = f(1) \\}$ is a subspace of $V$.