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Function such that f(x^2+1)^sqrt(x)=k

Source: 1978 AHSME Problem 17

June 6, 2014
functionAMC

Problem Statement

If kk is a positive number and ff is a function such that, for every positive number xx, [f(x2+1)]x=k;\left[f(x^2+1)\right]^{\sqrt{x}}=k; then, for every positive number yy, [f(9+y2y2)]12y\left[f(\frac{9+y^2}{y^2})\right]^{\sqrt{\frac{12}{y}}} is equal to
<spanclass=′latex−bold′>(A)</span>k<spanclass=′latex−bold′>(B)</span>2k<spanclass=′latex−bold′>(C)</span>kk<spanclass=′latex−bold′>(D)</span>k2<spanclass=′latex−bold′>(E)</span>yk<span class='latex-bold'>(A) </span>\sqrt{k}\qquad<span class='latex-bold'>(B) </span>2k\qquad<span class='latex-bold'>(C) </span>k\sqrt{k}\qquad<span class='latex-bold'>(D) </span>k^2\qquad <span class='latex-bold'>(E) </span>y\sqrt{k}
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