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If f(x) satisfies x+|f(x)|=2f(x) then f^-1(x) satisfies

If f(x) satisfies x+|f(x)|=2f(x) then f^-1(x) satisfies

Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
4 years ago
i am getting the answer as 
3x – |f–1 (x)|= 2f–1 (x) where f(x) is greater than equal to zero.
the reason is that if f(x) is greater than equal to zero, then |f(x)|= f(x) so that x+|f(x)|=2f(x) implies x+f(x)=2f(x) or f(x)=x. since f is greater than zero, hence x should also b greater than zero.
hence, f-1(x)= x which too is greater than zero.
now 3x – |f–1 (x)|= 3x – |x|= 3x – x= 2x= 2f–1 (x)
or 3x – |f–1 (x)|= 2f–1 (x)
kindly approve:)

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