If a function is affine and bounded on [0,1], does that mean: For all $x\in \mathbb{R}$, $0\leq f(x)\leq 1$? Or does it mean there exists $M,N \in \mathbb{R}$ such that for all $x\in [0,1]$, $N\leq f(x) \leq M$?
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3The second is the right one – Haha Nov 11 '13 at 00:04
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:D thanks friend – user101017 Nov 11 '13 at 00:07
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A function as bounded on an interval $I$ means that the funtion has a maximum value and a minimum value within that interval.
(In your statement, $[a,b]$ is a closed and bounded interval, so $f$ trivially has upper and lower bounds.)
JRC
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