The question is about approximating the continuous function in an interval $[a, b]$. If we consider the linear space of all such functions endowed with the norm
$$||f|| = \max_{x \in [a, b]}|f(x)|$$
then the best error approximating a function $f$ using polynomials $p \in \pi_n$ (with $\pi_n$ is denoted the set of all polynomials of degree $\leq n$) is
$$E_n(f) = \inf_{p\in \pi_n} ||f-p||$$
I need to show that $E_n(f + g) \leq E_n(f) + E_n(g)$. I don't know how to approach the problem. Any hints?