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The problem asks for the equation of the function \( f(x) = 2^{x-3} + 1 \) after a rotation of \(-90^\circ\) about the origin \((0, 0)\).

### Steps to solve:

1. **Understand the rotation effect**:  
   A rotation of \(-90^\circ\) about the origin switches the coordinates \((x, y)\) to \((-y, x)\).

2. **Initial equation**:  
   The given function is:
   \[
   f(x) = 2^{x-3} + 1
   \]
   which is in the form \( y = 2^{x-3} + 1 \).

3. **Apply rotation**:
   When rotating the graph of a function by \(-90^\circ\), the point \((x, y)\) transforms into \((y, -x)\). This changes the relationship between \(x\) and \(y\).

   Substitute \(x\) for \(y\) and \(-y\) for \(x\):
   \[
   x = 2^{-y-3} + 1
   \]
   
4. **Solve for \( y \)**:
   To rewrite this equation in terms of \(y\), first isolate the exponential term:
   \[
   x - 1 = 2^{-y-3}
   \]
   Take the logarithm (base 2) of both sides:
   \[
   \log_2(x - 1) = -y - 3
   \]
   Solving for \(y\):
   \[
   y = -(\log_2(x - 1) + 3)
   \]
   Simplify:
   \[
   y = -\log_2(x - 1) - 3
   \]

Thus, the equation of the rotated function is:
\[
y = -\log_2(x - 1) - 3
\]

Would you like further details or clarifications?

### Related Questions:
1. What is the effect of a \(90^\circ\) rotation instead of \(-90^\circ\)?
2. How does the function \( f(x) = 2^{x-3} + 1 \) behave graphically before rotation?
3. What is the transformation rule for other degrees of rotation (e.g., \(180^\circ\))?
4. How can we verify the result of a rotated function using geometry?
5. What would be the function equation after a reflection across the x-axis?

### Tip:
When transforming functions by rotation, remember that the coordinate changes (like \((x, y) \to (-y, x)\) for \(-90^\circ\)) help guide the process of rewriting the function equation.

Persamaan bayangan dari fungsi f(x) = 2^(x-3) + 1 akibat rotasi dengan pusat (0,0) sebesar -90° adalah ...

Learn how to find the equation of the function f(x) = 2^(x-3) + 1 after a -90° rotation about the origin. This problem covers exponential functions and geometric transformations with a step-by-step solution suitable for Grades 10-12.

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