Home Competitions AHSME 1983 Problem 18
Let f f f be a polynomial function such that, for all real x x x ,
f ( x 2 + 1 ) = x 4 + 5 x 2 + 3 f(x^2 + 1) = x^4 + 5x^2 + 3 f ( x 2 + 1 ) = x 4 + 5 x 2 + 3 .
For all real x , f ( x 2 − 1 ) x, f(x^2-1) x , f ( x 2 − 1 ) is
(A) x 4 + 5 x 2 + 1 (B) x 4 + x 2 − 3 (C) x 4 − 5 x 2 + 1 (D) x 4 + x 2 + 3 (E) none of these \textbf{(A)}\ x^4+5x^2+1 \textbf{(B)}\ x^4+x^2-3 \textbf{(C)}\ x^4-5x^2+1 \textbf{(D)}\ x^4+x^2+3 \textbf{(E)}\ \text{none of these} (A) x 4 + 5 x 2 + 1 (B) x 4 + x 2 − 3 (C) x 4 − 5 x 2 + 1 (D) x 4 + x 2 + 3 (E) none of these
Dataset text NuminaMath-1.5 . Quoted with source.
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