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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 $|f(x)|$

1 Answers 1

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Triangle inequality gives us

$|f(x)| \leq |f(x) - g(x)| + |g(x)| < \epsilon + M$

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    Your welcome then.2012-11-15