https://file.aiquickdraw.com/mathbot/file/1725917906598vajr01lz.jpg

The problem asks for the domain of the function \( g(x - 3) \), given that the domain of \( g(x) \) is \( -5 < x < 5 \).

### Step-by-Step Solution:

1. The original domain of \( g(x) \) is given as \( -5 < x < 5 \).
2. Now, we need to find the domain of \( g(x - 3) \).
3. To do this, let's replace \( x \) with \( x - 3 \) in the inequality for the domain:
   \[
   -5 < x - 3 < 5
   \]
4. To isolate \( x \), add 3 to all parts of the inequality:
   \[
   -5 + 3 < x - 3 + 3 < 5 + 3
   \]
   This simplifies to:
   \[
   -2 < x < 8
   \]

### Final Answer:
The domain of \( g(x - 3) \) is \( -2 < x < 8 \).

Would you like any more details or have any questions about this solution?

Here are some related questions for further exploration:
1. How does shifting a function horizontally affect its domain?
2. What would the domain be if the function were \( g(x + 2) \) instead of \( g(x - 3) \)?
3. How do you find the domain of a function that involves both a shift and a stretch?
4. How can you find the range of the function given its domain?
5. What happens to the domain if the original domain has restrictions like square roots or denominators?

**Tip**: When shifting a function horizontally by \( c \), the new domain will shift by \( c \) units in the opposite direction.

The domain of the function g(x) is -5 < x < 5. What is the domain of g(x - 3)?

Learn how to find the domain of the function g(x - 3), given that the domain of g(x) is -5 < x < 5. This problem covers function transformations and shifts, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation