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KCET2025MathematicsFunctions

Let the functions " f " and " g " be f : [0, 2 ] R given by f ( x )= x and g : [0, 2 ] R given by g(x)= x , where R is the set of real numbers Consider the following statements: Statement (I): f and g are one-one Statement (II): f + g is one-one Which of the following is correct?

Options

  1. AStatement (I) is true, statement (II) is false
  2. BStatement (I) is false, statement (II) is true
  3. CBoth statements (I) and (I) are true
  4. DBoth statements (I) and (II) are false

Correct answer

A. Statement (I) is true, statement (II) is false

Step-by-step solution

aligned & f : one - one [0, 2 ] R.f ( x )= x & ~g : one - one [0, 2 ] R.f ( x )= x aligned Statement I is true aligned & ( f + g ): [0, 2 ] R & f + g ( x )= x + x & . array l ( f + g )(0)=0 ( f + g )( / 2)=0 array f + g is not one - one aligned

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