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JEE Main2012MathematicsFunctionsActual

Let f(x)= x, g(x)=x . Statement 1: f(x) g x( for ) x in (0, ) Statement 2: f(x) 1 for x in (0, ) but g(x) as x .

Options

  1. AStatement 1 is true, Statement 2 is false.
  2. BStatement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.
  3. CStatement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
  4. DStatement 1 is false, Statement 2 is true.

Correct answer

C. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

Step-by-step solution

Let f(x)= x and g(x)=x Statement-1: f(x) g x( x) 0, ( ) i.e., x x x (0, ) which is true Statement-2: f(x) 1 x 0, ( ) i.e., x 1 x (0, ) It is true and g(x)=x as x also true.

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