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Most Important Selected Qs for JEE AdvancedMathematicsFunctions

If f: A B, f(x)= ⁻¹ ( [x] x ) and g: C D, g(x)= ⁻¹ ( [x] x ) , then which of the following is always correct? [Note: [ ] and denotes greatest integer and fractional part function respectively.]

Options

  1. AA=C
  2. Bf(x) and g(x) both are injective
  3. CB and D both are singleton sets
  4. DNumber of integral solution of the equation f(x)+g(x)= 2 is zero.

Correct answer

D. Number of integral solution of the equation f(x)+g(x)= 2 is zero.

Step-by-step solution

Clearly, f(x) and g(x) is defined if -1 [x] x 1 aligned & 0 x < 1 and [x] I & 0 < x < 1 [x] x =0 aligned A=C=(0,1) and f(x)=0 and g(x)= 2 x (0,1)B and D are co-domain Need not to be singleton sets. f(x)+g(x)= 2 x (0,1) No. of integral solution =0 .

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