Let `f(x)=(a_(2k)x^(2k)+a_(2k-1)x^(2k-1)+...+a_(1)x+a_(0))/(b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0))`, where k is a positive integer, `a_(i), b_(i) in R " and " a_(2k) ne 0, b_(2k) ne 0` such that `b_(2k)x^(2k)+b_(2k-1)x^(2k-1)+...+b_(1)x+b_(0)=0` has no real roots, then

Options

A. f(x) must be one to one
B. `a_(2k)x^(2k)+a_(2k-1)+...+a_(1)x+a_(0)=0`
must have real roots
C. f(x) must be many to one
D. Nothing can be said about the above options

Answer

C