Consider the function f(x) = 2 x - \cos(x) + 6 on the interval
0\le x\le 1 . The Intermediate Value Theorem guarantees that
for certain values of k there is a number c such that f(c)=k . In the case of the function above, what, exactly, does the intermediate value theorem say? To answer, fill in the following mathematical statements, giving
an interval with non-zero length in each case.

For every

there is a

such that

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