Function with Exponential

Algebra Level 2

f f is a function on the positive reals which satisfies the equation [f(x2+1)]x=16 \left[ f\left(x^2 +1 \right) \right]^{\sqrt{x}} = 16 . What is the value of

[f(16+y2y2)]1y? \large \left[ f\left( \frac {16+y^2} {y^2} \right) \right] ^{ \large{ \frac {1}{\sqrt{y}} } } ?

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