To find the related square root function \( p(x) \) for the quadratic equation \( h(x) = 4x^2 \) with the domain \( (0, \infty) \), we can express the function in terms of a square root.
The quadratic function \( h(x) = 4x^2 \) can be rewritten in terms of \( p(x) \) by taking the square root:
\[ p(x) = \sqrt{h(x)} = \sqrt{4x^2} \]
Simplifying this gives us:
\[ p(x) = 2x \]
Thus, we identify that:
\[ p(x) = ax \]
where \( a = 2 \).
So, for \( p(x) = ax \), we have:
\[ a = 2 \]
Final answer: \( a = 2 \)
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