JEE Mathematics/ Lakshmikanta Satapathy/ Relation and Function QA part 1/ JEE question on Domain of an even function solved with the related concepts

1. Physics Helpline
L K Satapathy
Relations & Functions QA 1

2. Physics Helpline
L K Satapathy
Relation Function 1
Question: If and , then S
Answer :
 1( ) 2 3 , 0f x f x x
x
    : ( ) ( )S x R f x f x   
(a) is an empty set (b) contains exactly one element
(c) contains exactly two elements (d) contains more than two elements
 1( ) 2 3 . . . (1)f x f x
x
 
Replacing x by (1/x) in (1)  1 32 ( )f f x
x x
 
 1 3 2 ( ) . . . (3)f f x
x x
  
  3 ( )1 . . . (2)
2
x f x
f
x

 
Given

3. Physics Helpline
L K Satapathy
Relation Function 1
Correct option = (c)
3 ( ) 3 2 ( )
2
x f x
f x
x

  
63 ( ) 4 ( )x f x f x
x
   
6 23 ( ) 3 ( )f x x f x x
x x
     
2 2( ) ( )f x f x x x
x x
      
242 2x x
x
   
 S has 2 elements
Equations (2) & (3)
Again
2x  

4. Physics Helpline
L K Satapathy
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