You are given the function $f(x) = x^2 - 2x + 2$, and you're asked to evaluate the function at $f(2x - 3)$.

This means you need to substitute $x$ in the function $f(x)$ with $2x - 3$. So, we replace every occurrence of $x$ in the formula with $2x - 3$.

Let's compute it:

$f(2x - 3) = (2x - 3)^2 - 2(2x - 3) + 2$

Now, expand and simplify the expression step by step.

Step 1: Expand $(2x - 3)^2$

$(2x - 3)^2 = (2x - 3)(2x - 3) = 4x^2 - 12x + 9$

Step 2: Expand $-2(2x - 3)$

$-2(2x - 3) = -4x + 6$

Step 3: Combine everything

$f(2x - 3) = 4x^2 - 12x + 9 - 4x + 6 + 2$

Step 4: Simplify the expression

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

Thus, the function evaluated at $f(2x - 3)$ is: $f(2x - 3) = 4x^2 - 16x + 17$

Would you like further details on this? Here are some related questions:

1. How do you evaluate functions at other variable substitutions?
2. Can we find the roots of the new function $f(2x - 3)$?
3. What is the vertex of the quadratic function $f(2x - 3)$?
4. How do transformations affect the graph of a function?
5. How do you compute the derivative of this function?

Tip: When substituting expressions into a function, always carefully replace every instance of the original variable with the new expression.