Skip to content / Đến nội dung
ThichHocToan.com

1981 AMC 12 Question 17

AMC12 · 1981 AMC 12

Question 17

The function $f$ is not defined for $x=0,$ but, for all nonzero real numbers $x,$ $$
f(x)+2f\left(\frac1x\right)=3x.
$$ The equation $f(x)=f(-x)$ is satisfied by
  1. exactly one real number
  2. exactly two real numbers
  3. no real numbers
  4. infinitely many, but not all, nonzero real numbers
  5. all nonzero real numbers