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1983 AMC 12 Question 18

AMC12 · 1983 AMC 12

Question 18

Let $f$ be a polynomial function such that, for all real $x,$ $$
f(x^2+1)=x^4+5x^2+3.
$$ For all real $x,$ $f(x^2-1)$ is
  1. $x^4+5x^2+1$
  2. $x^4+x^2-3$
  3. $x^4-5x^2+1$
  4. $x^4+x^2+3$
  5. none of these