Two functions f: R R, g: R R are defined as follows f(x)= cases 0, & x is rational 1, & x is irrational cases g(x)= array cc -1, & x is rational 0, & x is irrational array . Then, (f g)( )+(g f)(e) is equal to

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Correct answer: B. -1

aligned & (g f)(e)=g(f(e))=g(1)=-1 & (f g)( )=f(g( ))=f(-1)=0 & (f g)( )+(g f)(e)=0-1=-1 & aligned

Two functions f: R R, g: R R are defined as follows f(x)= cases 0, & x is rational 1, & x is irrational cases g(x)= array cc -1, & x is rational 0, & x is irrational array . Then, (f g)( )+(g f)(e) is equal to

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