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Let f(x)=x^2 + 3x-3,x leq 0. If n point...

Let `f(x)=x^2 + 3x-3,x leq 0`. If n points `x_1, x_2, x_3,.....,x_n` are so chosen on the x-axis such that
(1)`1/n sumf^-1(x_i)=f(1/n sum_( i=1 )^nx_i)`
(2) `sum_(i=1) ^ n f^-1(x_i)=sum_(i=1) ^ n x_i`where `f^-1` denotes the inverse of f, Then the AM of xi's is
a)1
b)2
c)3
d)4

Text Solution

Verified by Experts

The correct Answer is:
`1/n sum_(i=1)^(n)x_(i)=1`
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