Quotient of functions

16 Views Asked by At

I am trying to solve the following problem.

Define the vector space $V = \{\text{functions $f: \mathbb{R} \to \mathbb{R}$}\}$ and the subpsace $U \subset V$ by $U = \{\text{functions $f: \mathbb{R} \to \mathbb{R} \mid f(0) = 0$}\}$. Prove that the quotient $V/U$ is finite-dimensional and compute $\dim (V/U)$.

I cannot figure out how to get started. Any help would be appreciated.