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AP EAMCET20225 Jul 2022Morning ShiftMathematicsFunctionsActual

f(x)= ( ( 2 x^2-3 x )+ 4 x^4-11 x^2+9 |x| ) is

Options

  1. Aan odd function
  2. Ban even function
  3. Ca polynomial function
  4. Dnot a function

Correct answer

A. an odd function

Step-by-step solution

f(x)= ( ( 2 x^2-3 x )+ 4 x^4-11 x^2+9 |x| ) aligned & f(-x)= ( 2(-x)^2-3 (-x) + 4(-x)^4-11(-x)^2+9 |-x| ) & f(-x)= [ 2 x^2-3 -x + 4 x^4-11 x^2+9 |x| ] aligned We know that, if function f(x) is an odd function. Then, f(x)+f(-x)=0 aligned & = [ 4 x^4-11 x^2+9 x^2 - (2 x^2-3 )^2 x^2 ] & = [ 4 x^4-11 x^2+9-4 x^4-9+12 x^2 x^2 ] & = 1=0 aligned

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