To solve for $f(2x - 3)$ given the function $f(x) = x^2 - 2x + 2$, we'll substitute $2x - 3$ in place of $x$ in the function.

1. Start with the original function: $f(x) = x^2 - 2x + 2$

2. Substitute $2x - 3$ for $x$: $f(2x - 3) = (2x - 3)^2 - 2(2x - 3) + 2$

3. Expand and simplify: $(2x - 3)^2 = (2x - 3)(2x - 3) = 4x^2 - 12x + 9$ $-2(2x - 3) = -4x + 6$

4. Combine all the terms: $f(2x - 3) = 4x^2 - 12x + 9 - 4x + 6 + 2$ $f(2x - 3) = 4x^2 - 16x + 17$

So, $f(2x - 3) = 4x^2 - 16x + 17$.

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

Here are 5 related questions you might find interesting:

1. What is the derivative of the function $f(x) = 4x^2 - 16x + 17$?
2. How would you find the vertex of the parabola represented by $f(2x - 3)$?
3. How do you determine if the function $f(x) = 4x^2 - 16x + 17$ has any real roots?
4. Can you find the y-intercept of the function $f(2x - 3)$?
5. How does the transformation of $f(x) = x^2 - 2x + 2$ to $f(2x - 3)$ affect its graph?

Tip: When substituting expressions into functions, always remember to fully expand and simplify the terms to avoid errors in calculations.