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AP EAMCET202418 May 2024Morning ShiftMathematicsFunctionsActual

If a function f: R R is defined by f(x)=x^3-x , then f is

Options

  1. Aone-one and onto
  2. Bone-one but not onto
  3. Conto but not one-one
  4. Dneither one-one nor onto

Correct answer

C. onto but not one-one

Step-by-step solution

Given f: R R such that f(x)=x^3-x=x(x-1)(x+1) f(1)=0=f(0) . So, f(x) is not one-one Since, f(x)=x^3-x is a polynomial function So it is continuous on R and, If x f(x) and x - f(x) - . So, range of f(x) is (- , ) f(x) is an onto function

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