Half root (corrected)

Algebra Level 4

Let $f: \mathbb{R}^+ \to \mathbb{R}^+$ be a positive, monotonically increasing function with the property $f\big(f(x)\big) = \sqrt{x}.$ What is the value $f (2)$ ?

Cannot be determined

2^ \frac{2}{3}

2^ \frac{\sqrt{2}}{2}

2^ \frac{3}{4}

2^ \frac{1}{2}