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Paragraph: Let f be a function defined so that every element of the co-domain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as "two-one" function. A two-one function is definitely a many one function but vice-versa is not true. For example, y= |e^x-1 | is a "two-one" function. y=x^3-x is a many one function but not a "two-one

Options

  1. Ay=| | x
  2. By=x^2 x
  3. Cy=x^3+3 x+1
  4. Dy=x^4-x+1

Correct answer

D. y=x^4-x+1

Step-by-step solution

y=| n| x|| has graph here an element in co-domain can have 4 pre-images y=x^2 x is zero for infinitely many values of xy=x^3+3 x+1 is M.I. and hence one-one function y=x^4-x+1 has graph y = x ^4- x +1 is two-one

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