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.

Here are the solutions to the questions: 4. The functions f and g are defined by f(x) = (1)/(x−3), x ∈ R, x ≠ 3 and g(x) = √(x+1), x ∈ R, x ≥ −1. a) Find f⁻¹(x) and state its domain. Step 1: Let y = f(x). So, y = (1)/(x−3). Step 2: To find the inverse function, swap x and y: x = (1)/(y−3) Step 3

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.

Here are the solutions to the questions: 4. The functions f and g are defined by f(x) = (1)/(x−3), x ∈ R, x ≠ 3 and g(x) = √(x+1), x ∈ R, x ≥ −1. a) Find f⁻¹(x) and state its domain. Step 1: Let y = f(x). So, y = (1)/(x−3). Step 2: To find the inverse function, swap x and y: x = (1)/(y−3) Step 3

Solved: The functions f and g are defined by f(x)…

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.

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.

Step-by-step solution

Let $y = f(x)$ .

To find the inverse function, swap $x$ and $y$

Step 3

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