Difference between revisions of "1983 AHSME Problems/Problem 18"
Line 3: | Line 3: | ||
<cmath>f(x^2 + 1) = x^4 + 5x^2 + 3.</cmath> | <cmath>f(x^2 + 1) = x^4 + 5x^2 + 3.</cmath> | ||
For all real <math>x</math>, <math>f(x^2 - 1)</math> is | For all real <math>x</math>, <math>f(x^2 - 1)</math> is | ||
+ | |||
+ | (A) <math>x^4 + 5x^2 + 1</math> (B) <math>x^4 + x^2 - 3</math> (C) <math>x^4 - 5x^2 + 1</math> (D) <math>x^4 + x^2 + 3</math> (E) none of these | ||
Solution: | Solution: | ||
− | + | ||
Let <math>y = x^2 + 1</math>. Then <math>x^2 = y - 1</math>, so we can write the given equation as | Let <math>y = x^2 + 1</math>. Then <math>x^2 = y - 1</math>, so we can write the given equation as | ||
\begin{align*} | \begin{align*} |
Revision as of 13:55, 1 July 2017
Problem: Let be a polynomial function such that, for all real , For all real , is
(A) (B) (C) (D) (E) none of these
Solution:
Let . Then , so we can write the given equation as