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KCET2023MathematicsFunctions

f : R R and g:[0, ) R defined by f(x)=x^2 and g(x)= x . Which one of the following is not true?

Options

  1. A(f g)(-4)=4
  2. B(f g)(2)=2
  3. C(g f)(-2)=2
  4. D(g f)(4)=4

Correct answer

A. (f g)(-4)=4

Step-by-step solution

f o g(x)=f(g(x)) As domain of g(x) [0, ) , so domain of f g( ) also [0, ) f(g(x))=( x )^2 aligned & g f(x)=g(f(x)) & g f(x)= x^2 =|x| aligned Hence, f o g(-4)=( -4 )^2 is not define.

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