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Most Important Selected Qs for JEE AdvancedMathematicsFunctions

Find the domain of the following functions array |c|c|c|c| |r| Column - I & |r| Column - II (A) & f(x)= & (p) & n , n Z & [x] & & (B) & f ( x )= x & (q) & [2, x) (C) & f ( x )= ⁻¹ ( ₂ x ) & (r) & x Z (D) & f ( x )= ₃(( x ) & (s) & [ 1 2 2 ] & & (1) & R - L array

Options

  1. A( A ) ( q ) ;( B ) ( t ) ;( C ) ( s ) ;( D ) ( p )
  2. B( A ) ( p ) ;( B ) ( q ) ;( C ) ( r ) ;( D ) ( s )
  3. C( A ) ( r ) ;( B ) ( s ) ;( C ) ( q ) ;( D ) ( p )
  4. D( A ) ( s ) ;( B ) ( p ) ;( C ) ( r ) ;( D ) ( q )

Correct answer

A. ( A ) ( q ) ;( B ) ( t ) ;( C ) ( s ) ;( D ) ( p )

Step-by-step solution

(A) f(x)= 1 [x] ,[x] 0 and [x] 1 (As for |x|=1, |x|=0 ) |x| 2 x 2, ) (B) f(x)= x is defined as x 0 which is true for all real number except integers. Hence the domain is R - z . (C) f(x)= ^ ( x) . Domain of ⁻¹ x is [-1,1] . Therefore - 1 ₂ x 1 aligned & 2⁻¹ x 2 & 1 2 x 2, x [ 1 2 , 2 ] aligned (D) f(x)= ₃(( x) f ( x ) is defined only if ₃( x ) 0, ( x ) 1 aligned & ( x) 1 as -1 0 1 & x=0 x=n , n I aligned Hence, the domain consists of the multiple of , i.e. Domain = n , n I

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