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AP EAMCET2012MathematicsFunctions

If f: R R^2 and g: R⁺ R are such that g f(x) =| x| and f g(x) =( x )^2 , then a possible choice for f and g is

Options

  1. Af(x)=x^2, g(x)= x
  2. Bf(x)= x, g(x)=|x|
  3. Cf(x)= ^2 x, g(x)= x
  4. Df(x)=x^2, g(x)= x

Correct answer

C. f(x)= ^2 x, g(x)= x

Step-by-step solution

Given, g f(x) =| x| and f g(x) =( x )^2 Let us consider f(x)= ^2 x and g(x)= x f g(x) =f( x )= ( ^2 x )=( x )^2 and g f(x) =g ( ^2 x )= ^2 x =| x|

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