Find a rational function f : R → R with range f(R) = [-1, 1]. (Thus f(x) = P(x)

Question

/Q(x) for
all x belongs R for suitable polynomials P and Q where Q has no real root).

R(real numbers)

Answer 1

well, let's see

x/(x^2+1) has range [-.5,.5], so

f(x) = 2x/(x^2+1)