Given the inequalities:
$$|f(x) - g(x)| < \epsilon\quad \forall \quad x \in [a,b]$$
and
$$|g(x)| < M \quad \forall \quad x \in [a,b]$$
where $\epsilon > 0$ and $M > 0$.
What is the tightest bound that I can get on $|f(x)|$
Given the inequalities:
$$|f(x) - g(x)| < \epsilon\quad \forall \quad x \in [a,b]$$
and
$$|g(x)| < M \quad \forall \quad x \in [a,b]$$
where $\epsilon > 0$ and $M > 0$.
What is the tightest bound that I can get on $|f(x)|$
Triangle inequality gives us
$$|f(x)| \leq |f(x) - g(x)| + |g(x)| < \epsilon + M$$