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AP EAMCET20228 Jul 2022Evening ShiftMathematicsFunctionsActual

If the function f: R R is defined by f(x)=x|x| , then .

Options

  1. Af is one-one but not onto
  2. Bf is onto but not one-one
  3. Cf is both one-one and onto
  4. Df is neither one-one nor onto

Correct answer

C. f is both one-one and onto

Step-by-step solution

Given, f(x)=x|x|= array l x(x), x 0 x(-x), x According to the graph, domain of f(x)= Range of f(x)=R Range = Codomain =R f(x) is an onto function. If a line parallel to X -axis is drawn, it will intersect at only one point of f(x) . Hence, f(x) is one-one also.

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