(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let f : R -> R be a continuous function such that f(0) = 0. If S := {f(x) | x in R} is not

bounded above, prove that [0, infinity) ⊆ S (that is, S contains all non-negative real numbers).

Then find an appropriate value for a in the Intermediate Value theorem.

2. Relevant equations

3. The attempt at a solution

If y > 0, then since S is not bounded above, there exists b in R such that f(b) > y.

Then because y>0 , f(b) >0 and [0, infinity) ⊆ S ????

Applying the intermediate value theorem to this continuous function, it follows that there exists a real number a such that f(a) = y. ????

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# Homework Help: Continuous not bounded above function

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