smc

If $k$ is a positive number and $f$ is a function such that, for every positive number $x$, ${\left[f(x^2+1)\right]}^{\sqrt{x}}=k$; then, for every positive number $y$, ${\left[f(\frac{9+y^2}{y^2})\right]}^{\sqrt{\frac{12}{y}}}$ is equal to