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JEE Main20245 Apr 2024Evening ShiftMathematicsFunctionsActual

Let f, g: R R be defined as : f(x)=|x-1| and g(x)= cases e ^x, MARA & x 0 x+1, & x 0 cases Then the 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

A. neither one-one nor onto.

Step-by-step solution

aligned & f(g(x))=|g(x)-1| & f o g [ array cc |e^x-1 | & x 0 |x+1-1| & x 0 array . & fog [ array cc e^x-1 & x 0 -x & x 0 array . aligned

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