Find the domain and range of the real-valued function $f(x) = \sqrt{16 - x^2}$.

If $f(x) = \frac{2x + 1}{3x - 4}$ for $x \ne \frac{4}{3}$, find the inverse function $f^{-1}(x)$ and verify that $(f \circ f^{-1})(x) = x$.

Let $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = 2x - 3$ and $g: \mathbb{R} \to \mathbb{R}$ defined by $g(x) = x^2$. Determine whether each function is (i) injective (one-to-one), (ii) surjective (onto), or (iii) bijective.

Let $f(x) = \frac{2x + 1}{x - 3}$ ($x \ne 3$). (a) Find the inverse function $f^{-1}(x)$. (b) State the domain and range of $f^{-1}(x)$. (c) Verify that $(f \circ f^{-1})(x) = x$.