Questions: The domain of a one-to-one function f is [7, ∞), and its range is [-2, ∞). State the domain and the range of f^-1. What is the domain of f^-1 ? The domain of f^-1 is . (Type your answer in interval notation.)

The domain of a one-to-one function f is [7, ∞), and its range is [-2, ∞). State the domain and the range of f^-1.

What is the domain of f^-1 ?
The domain of f^-1 is .
(Type your answer in interval notation.)

Transcript text: The domain of a one-to-one function $f$ is $[7, \infty)$, and its range is $[-2, \infty)$. State the domain and the range of $f^{-1}$. What is the domain of $f^{-1}$ ? The domain of $\mathrm{f}^{-1}$ is $\square$. (Type your answer in interval notation.)

Solution

Solution Steps

Step 1: Identify the Domain and Range of $f$

The domain of $f$ is given as $[7, \infty)$ and the range of $f$ is given as $[-2\infty)$

Step 2: Swap the Domain and Range for $f^{-1}$

Since the inverse function $f^{-1}$ reverses the roles of inputs and outputs, the domain of $f^{-1}$ will be the range of $f$, and the range of $f^{-1}$ will be the domain of $f$. Therefore, the domain of $f^{-1}$ is $[-2\infty)$ and the range of $f^{-1}$ is $[7, \infty)$.