Most Important Selected Qs for JEE AdvancedMathematicsFunctions

Let a function f(x), x 0 be such that f(x)+f ( 1 x )=f(x) f ( 1 x ) then f(x) can be :

Options

A1-x²⁰¹³
B|x| +1
C2 ⁻¹|x|
D2 1+ k | x | , k being arbitrary constant

Correct answer

D. 2 1+ k | x | , k being arbitrary constant

Step-by-step solution

A & B are obvious aligned & ( f ( 1 x )-1 )= 1 ( f ( x )-1) i.e., ( f ( 1 x )-1 ) isreciprocal of ( f ( x )-1) & Now, forf f ( x )= / 2 ⁻¹| x | , f ( x )-1= ⁻¹| x | ⁻¹| x | , f ( 1 x )-1= ⁻¹| x | ⁻¹| x | & Alsofor f ( x )= 2 1+ k n | x | , f ( x )-1= 1- k n | x | 1+ k n | x | f ( 1 x )-1= 1+ k n | x | 1- k n | x | aligned

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