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AP EAMCET202018 Sep 2020Evening ShiftMathematicsFunctionsActual

The function of (f(x)=|x|+ |x| x ) is

Options

  1. Acontinuous at the origin
  2. Bdiscontinuous at the origin because (|x| ) is discontinuous there
  3. Cdiscontinuous at the origin because ( |x| x ) is discontinuous there
  4. Ddiscontinuous at the origin because both (|x| ) and ( |x| x ) are discontinuous

Correct answer

C. discontinuous at the origin because ( |x| x ) is discontinuous there

Step-by-step solution

(f(x)=|x|+ |x| x ) LHL of (x=0 ) ( aligned _ x 0⁻ f(x) & = _ x 0⁻ -x+ -x x & = _ x 0⁻ -x-1=-1 _ x 0⁺ f(x) & = _ x 0⁺ (x)+ (x) x & = _ x 0⁺ x+1=1 aligned ) ( ) LHL ( ) RHL at (x=0 ) ( f(x) ) is discontinuous at (x=0 ) Hence, option (c) is correct.

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