The domain of a​ one-to-one function g is

left parenthesis negative infinity comma 0 right bracket(−∞,0]​,

and its range is

left bracket 4 comma infinity right parenthesis[4,∞).

State the domain and the range of

gSuperscript negative 1−1.

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Part 1

The domain of

gSuperscript negative 1−1

is

enter your response here.

​(Type your answer in interval​ notation.)

For a function \( g \), the domain of its inverse function \( g^{-1} \) is the range of the original function \( g \), and the range of \( g^{-1} \) is the domain of \( g \).

Given:

- Domain of \( g \): \( (-\infty, 0] \)
- Range of \( g \): \( [4, \infty) \)

The domain of \( g^{-1} \) will be the range of \( g \), which is \( [4, \infty) \).

### Final Answer:
The domain of \( g^{-1} \) is \( [4, \infty) \).

Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you find the range of an inverse function?
2. What are the conditions for a function to have an inverse?
3. How does the graphical representation of a function relate to its inverse?
4. Can a function with a restricted domain have an inverse?
5. What does it mean for a function to be one-to-one?

**Tip**: A function is one-to-one if it passes both the horizontal and vertical line tests, meaning each \( y \)-value corresponds to exactly one \( x \)-value.

The domain of a one-to-one function g is (-∞, 0], and its range is [4, ∞). State the domain and the range of g⁻¹.

Understand how to find the domain and range of an inverse function g⁻¹ when the domain of g is (-∞, 0] and the range is [4, ∞). This step-by-step explanation covers inverse functions, the relationship between domain and range, and the Inverse Function Theorem. Suitable for high school students in Grades 10-12.

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