4. The functions f and g are defined by f(x) = (1)/(x-3), x R, x 3 and g(x) = sqrt(x+1), x R, x -1.
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Here are the solutions to the questions:
4. The functions $f$ and $g$ are defined by $f(x) = \frac{1}{x-3}$, $x \in \mathbb{R}, x \ne 3$ and $g(x) = \sqrt{x+1}$, $x \in \mathbb{R}, x \ge -1$.
a) Find $f^{-1}(x)$ and state its domain.
Step 1: Let $y = f(x)$. So, $y = \frac{1}{x-3}$.
Step 2: To find the inverse function, swap $x$ and $y$:
$$x = \frac{1}{y-3}$$
Step 3
