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

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 $(f \circ f^{-1})(x) = x$.

Find the domain and range of the following real-valued functions: (a) $f(x) = \sqrt{9 - x^2}$ (b) $g(x) = \frac{1}{x^2 - 4}$ (c) $h(x) = \frac{x}{1 + x^2}$