Question

For each question below, find the inverse of the given equation. ● Use the answer key to determine that you accurately answered each question. ● If necessary, revise your work. 1. y = –2(x – 2) 2

Answer 1

To find the inverse of the given equation \( y = -2(x - 2) + 2 \), follow these steps:

1. **Switch x and y**: Replace \( y \) with \( x \) and \( x \) with \( y \).
\[
x = -2(y - 2) + 2
\]

2. **Solve for y**:
- Start by isolating the term with \( y \):
\[
x - 2 = -2(y - 2)
\]
- Divide both sides by -2:
\[
y - 2 = -\frac{x - 2}{2}
\]
\[
y - 2 = -\frac{x}{2} + 1
\]
- Add 2 to both sides:
\[
y = -\frac{x}{2} + 1 + 2
\]
\[
y = -\frac{x}{2} + 3
\]

3. **Write the inverse function**:
Thus, the inverse \( f^{-1}(x) \) is given by:
\[
f^{-1}(x) = -\frac{x}{2} + 3
\]

So, the final answer for the inverse of the equation \( y = -2(x - 2) + 2 \) is:
\[
\boxed{f^{-1}(x) = -\frac{x}{2} + 3}
\]