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JEE Main202124 Feb 2021Morning ShiftMathematicsFunctionsActual

Let f : R → R be defined as f x = 2 x - 1 and g : R - 1 → R . be defined as g x = x - 1 2 x - 1 . Then the composition function f g x is:

Options

  1. Aneither one-one nor onto
  2. Bone-one but not onto
  3. Conto but not one-one
  4. Dboth one-one and onto

Correct answer

B. one-one but not onto

Step-by-step solution

f g x = 2 g x - 1 = 2 2 x - 1 2 x - 1 - 1 . = x x - 1 = 1 + 1 x - 1 Range of f g x = R - 1 Range of f g x is not onto & f g x is one-one So f g x is one-one but not onto. one-one, into

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