Q1 f:R→ R ;f(x) is continuous funciton satisfying f(x)+f(x2)=2 for all x ε R,the f(x) is
a)into
b)many one
c)constatn
d)periodic
Q2 If [x] denotes GINT and f(x) =[n+p.sinx],0<x<π ,n ε I and p is a prime no., If p=19 the find total no. of points where f(x) is not diff
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UP 0 DOWN 0 0 2
2 Answers
11Ans 2) 37 ???
[n + p sinx] is not diff at those pts where n + p sinx is an integer.
i.e is sinx = 1, -1, r/p where 0 ≤ r ≤ p-1
or x = pie/2 , - pie/2 , sin -1 (r/p) , pie - sin -1 (r/p)
But x ≠- pie/2 , 0
Therefore, the function is not diff at x = pie/2 , sin -1 (r/p) , pie - sin -1 (r/p)
So, the reqd no. of points are 1 +2 (p-1) = 2p-1
So, if p = 19, then ans is 37
Anyways, this ques can also be solved with the help of grpah.
