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Manipal MET2014MathematicsFunctions

If f g=| x| and g f= ^2 x , then f(x) and g(x) are

Options

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

Correct answer

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

Step-by-step solution

aligned & f g=f g(x) =| x|= ^2 x & Also, g f=g f(x) = ^2 x & Obviously, ^2 x = g(x) & and ^2 x = ^2 f(x) & i.e., g(x)= ^2 x & and f(x)= x aligned

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