June 2nd, 2017, 10:50 AM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 232 Thanks: 2  Continuous function
1. If $\displaystyle f:[1,2] \rightarrow R $ is continuous and $\displaystyle f(1) < f(0) $, then A) $\displaystyle f([0,1]) \subseteq [f(1),f[0)]$. B) $\displaystyle f([0,1]) \supseteq [f(1),f[0)]$. C) $\displaystyle f([0,1]) = [f(1),f[0)]$. D) $\displaystyle f([0,1])$ need not be a closed interval. Please someone help to solve these kinds of problems like comparing two values 
June 2nd, 2017, 11:47 AM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,308 Thanks: 2443 Math Focus: Mainly analysis and algebra 
First, clearly determine the meaning of the notation. This is especially critical for A, B and C. Second, since D is significantly different than the rest, can you eliminate it or accept it? 

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