Answer:
To find \( (f \circ g)(x) \), we need to first find \( g(x) \) and then plug it into \( f(x) \).
Given:
\[ g(x) = \sqrt{48x} \]
Now, let's find \( f(g(x)) \):
\[ f(g(x)) = f(\sqrt{48x}) = \sqrt{3(\sqrt{48x})} \]
Simplify under the square root:
\[ \sqrt{3(\sqrt{48x})} = \sqrt{3 \cdot \sqrt{16 \cdot 3x}} = \sqrt{3 \cdot 4 \cdot \sqrt{3x}} = \sqrt{12 \cdot \sqrt{3x}} \]
\[ = \sqrt{12} \cdot \sqrt{\sqrt{3x}} = 2\sqrt{3} \cdot \sqrt[4]{3x} \]
So, \( (f \circ g)(x) = 2\sqrt{3} \cdot \sqrt[4]{3x} \).
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