Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability

Let f(x)= ⁻¹( 2 x) and g(x)=| x| then

Options

Anumber of solution of f(x)=g(x) in [0,2 ] is 4 .
Bf(x), g(x) is a periodic function
Cf(x), g(x) is a non differentiable function for some x ,
Df ( x ), g ( x ) is an even function

Correct answer

D. f ( x ), g ( x ) is an even function

Step-by-step solution

f(x)= ⁻¹( 2 x), g(x)=| x|f(x) , and g(x) both are even and periodic so max f(x), g(x) and f(x), g(x) will also be periodic and even. but f(x), g(x) will be non-differentiable when f(x)=g(x) no of points where f(x)=g(x) are four in [0,2 ]

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