Find the inverse of the function.
y=x–3
Write your answer in the form ax+b. Simplify any fractions.


To find the inverse of the function \( y = x - 3 \), follow these steps:

1. **Rewrite the function as** \( y = x - 3 \).
2. **Swap** \( x \) and \( y \): 
   \[
   x = y - 3
   \]
3. **Solve for** \( y \):
   \[
   y = x + 3
   \]

So, the inverse of the function is \( y = x + 3 \), which is in the form \( ax + b \), where \( a = 1 \) and \( b = 3 \).

Would you like a deeper explanation on any step or have questions? Here are 5 related questions:

1. How do you find the inverse of a quadratic function?
2. Can the inverse of any function always be found?
3. What happens if a function's inverse is not a function?
4. How does the domain and range change when finding the inverse of a function?
5. What are the graphical implications of a function and its inverse?

**Tip:** When finding inverses, always make sure the original function is one-to-one (passes the horizontal line test) to guarantee the inverse is a function.

Find the inverse of the function. y = x - 3. Write your answer in the form ax + b. Simplify any fractions.

Learn how to find the inverse of the linear function y = x - 3. This step-by-step solution explains the concept of function inversion, including key algebraic techniques such as swapping variables and solving for y. Suitable for students in Grades 9-11.

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