Let be a continuous function with the properties that and .What is the value of ?

Question

​Let  be a continuous function with the properties that  and  .What is the value of  ? ​

Quizplus · Accepted Answer

Since the function is continuous and has the property that 11eac44f_ee18_6d45_bedf_87869e6a9be6_TB7497_11, we know that there exists some point in the interval (0,1) where the function is equal to 1. Since the function also has the property that 11eac44f_ee18_9456_bedf_9b21d9528097_TB7497_11, we know that there exists some point in the interval (1,∞) where the function is equal to 1. Since the function is continuous and can't jump from 0 to 1 or from 1 to 0, it follows that the function must take on every value between 0 and 1 at some point in the interval (0,1) and every value between 1 and ∞ at some point in the interval (1,∞). Thus, the only conclusion we can draw is that 11eac44f_ee18_9457_bedf_eb47cd9c411a_TB7497_11 = 1.

​Let Be a Continuous Function with the Properties That

Let Be a Continuous Function with the Properties That