Let's find the inverse of the function $y = x + 8$.

Step 1: Switch $x$ and $y$

To find the inverse of a function, we switch $x$ and $y$, then solve for $y$: $x = y + 8$

Step 2: Solve for $y$

Isolate $y$: $y = x - 8$

Step 3: Express the inverse in the required form

We need to express the inverse function in the form $a(bx + c)^2 + d$. However, the given function is linear, not quadratic. Thus, rewriting it in quadratic form as requested is impossible since the inverse is simply a line. Therefore, the inverse function is: $y = x - 8$

Step 4: Domain of the inverse

Since there are no restrictions on $x$ in the original function, the domain of the inverse function is all real numbers. So, the domain can be written as $x \geq -\infty$.

However, since you asked for the domain in a specific form, we can write: $x \geq -\infty$ which encompasses all real numbers.

Summary:

• Inverse function: $y = x - 8$
• Domain of the inverse: $x \geq -\infty$

Would you like further details, or do you have any questions?

Here are 5 related questions:

1. How do you find the inverse of a quadratic function?
2. What is the domain of a function's inverse when the original function is a parabola?
3. Can a linear function have an inverse that is not linear?
4. What happens to the range of the original function when finding the inverse?
5. How can you verify if two functions are inverses of each other?

Tip: The domain of the inverse function is the range of the original function.