translate this into regular form

Question

- **Domain of \( f^{-1} \)**: \( \mathbb{R} \setminus \{0\} \)
- **Range of \( f^{-1} \)**: \( \mathbb{R} \setminus \left\{-\frac{2}{3}\right\} \)

Answer 1

To express the given information about the inverse function \( f^{-1} \) in a more regular format:

• Domain of \( f^{-1} \): The domain is all real numbers except 0, which can be written as:
  \( \text{Domain of } f^{-1} = (-\infty, 0) \cup (0, \infty) \)

• Range of \( f^{-1} \): The range is all real numbers except \(-\frac{2}{3}\), which can be written as:
  \( \text{Range of } f^{-1} = (-\infty, -\frac{2}{3}) \cup (-\frac{2}{3}, \infty) \)

Thus, in regular form you can state:

Domain of \( f^{-1} \): \( (-\infty, 0) \cup (0, \infty) \)
Range of \( f^{-1} \): \( (-\infty, -\frac{2}{3}) \cup (-\frac{2}{3}, \infty) \)