Convergence in a normed vector space - Linear operator

Nov 2018
4
0
Canada
Having X a normed vector space. If f is a linear operator from X to ℝ and is not continuous in 0 (element of X) , how can we show that there exists a sequence xn that converges to 0 for which we have f(xn) = 1 (for all n element of ℕ).
Any help would be greatly appreciated, thank you.