74 votes 74 votes A function $f(x)$ is continuous in the interval $[0,2]$. It is known that $f(0) = f(2) = -1$ and $f(1) = 1$. Which one of the following statements must be true? There exists a $y$ in the interval $(0,1)$ such that $f(y) = f(y+1)$ For every $y$ in the interval $(0,1)$,$f(y)$ = $f(2-y)$ The maximum value of the function in the interval $(0,2)$ is $1$ There exists a $y$ in the interval $(0,1)$ such that $f(y)$ = $-f(2-y)$ Calculus gatecse-2014-set1 calculus continuity normal + – go_editor asked Sep 28, 2014 go_editor 20.7k views answer comment Share Follow See all 7 Comments See all 7 7 Comments reply Show 4 previous comments DebRC commented Nov 21, 2022 reply Follow Share @MANSI_SOMANI Think of the function f(x) graphically, 8 votes 8 votes Ray Tomlinson commented Oct 10, 2023 i edited by Ray Tomlinson Oct 10, 2023 reply Follow Share One Answer will clear every doubt https://gateoverflow.in/1925/gate-cse-2014-set-1-question-47?show=412885#a412885 1 votes 1 votes gvinay commented Nov 20, 2023 reply Follow Share watch this …..defentely you get solution...it is in bangali language but it is easy to understand… https://www.youtube.com/watch?v=G9LLmDv3EIs thank youu soo much. 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes Option A is Correct but D is Wrong , Reason The difference between y and 2-y should be less than the length of the interval given . Difference between y and 2-y is 2 and length of interval is (0,1) Therefore D is Wrong pC answered Jan 14, 2016 pC comment Share Follow See all 11 Comments See all 11 11 Comments reply Show 8 previous comments Xylene commented Jul 29, 2017 reply Follow Share What is that theorem ? How to apply it here? Can you please explain ? @Kaluti 0 votes 0 votes bharti commented Aug 27, 2017 i edited by bharti Aug 27, 2017 reply Follow Share @xylene the Theorem is if g (x) is some function which is defined over a close interval(a,b) than the value of resultant function will always pass through (a,b). http://mathworld.wolfram.com/IntermediateValueTheorem.html 1 votes 1 votes Prasanna Kapil commented Oct 23, 2017 i edited by Prasanna Kapil Oct 23, 2017 reply Follow Share i think A & D both are correct as explained by Shreya 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes This Answer contains the all concept in which students having doubt and the usefull comments are also included so that the correct answer is option A and D. Ray Tomlinson answered Oct 10, 2023 Ray Tomlinson comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes One of better solution you can find from here..it is in english+bengali language but easy to understand. https://www.youtube.com/watch?v=G9LLmDv3EIs thank you soo much gvinay answered Nov 20, 2023 gvinay comment Share Follow See all 0 reply Please log in or register to add a comment.