If is a continuous function on the closed interval ,with and c is in the closed interval ,then which of the following statements must be true?

Question

​If  is a continuous function on the closed interval  ,with  and c is in the closed interval  ,then which of the following statements must be true? ​

Quizplus · Accepted Answer

This follows from the Intermediate Value Theorem, which states that if f(x) is continuous on the closed interval [a,b] and k is any number between f(a) and f(b), then there exists at least one value c in [a,b] such that f(c) = k. In this case, f(x) is continuous on the closed interval [a,b], where a and b are given by the problem (note that there was a typo in the original question, where b was given as 11eac44f_edd3_273f_bedf_3f493c3fb568_TB7497_11 instead of 11eac44f_edd3_274f_bedf_3f493c3fb568_TB7497_11), and k is the value given by 11eac44f_edd3_7464_bedf_21f58bc5d813_TB7497_11. Therefore, by the Intermediate Value Theorem, there must exist at least one value c in [a,b] such that f(c) = k, which corresponds to choice C. The other choices are not necessarily true based on the information given.

​If Is a Continuous Function on the Closed Interval

If Is a Continuous Function on the Closed Interval