Function with Exponential

Algebra Level 2

$$f$$ is a function on the positive reals which satisfies the equation $$\left[ f\left(x^2 +1 \right) \right]^\sqrt{x} = 16$$. What is the value of

$\large \left[ f\left( \frac {16+y^2} {y^2} \right) \right] ^{ \large{ \frac {1}{\sqrt{y}} } } ?$

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