https://file.aiquickdraw.com/mathbot/file/17259054487655x5fdd9k.jpg

The question in the image asks:

**Given:**  
\( f(x+1) = x^2 + 2x + 1 \)

**Find:**  
\( f(3) \)

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### Solution:

To find \( f(3) \), notice that the given expression is \( f(x+1) \), so we can set \( x+1 = 3 \).  
Thus, \( x = 2 \).

Now, substitute \( x = 2 \) into the expression for \( f(x+1) \):

\[
f(x+1) = x^2 + 2x + 1
\]

Substitute \( x = 2 \):

\[
f(3) = (2)^2 + 2(2) + 1 = 4 + 4 + 1 = 9
\]

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Therefore, \( f(3) = 9 \). However, none of the answer options (1, 2, 3, 4) are correct according to the calculation. There might be a typo in the question or options.

Do you want more details or explanations about this? Here are five questions that could help expand your understanding:

1. How do you handle different types of function transformations like \( f(x+1) \)?
2. What are common mistakes when interpreting shifted function inputs?
3. How do you approach problems when none of the provided options match the correct answer?
4. What is the general method for solving \( f(a) \) when given \( f(x+1) \) or similar forms?
5. Can the method of completing the square help in function transformations?

**Tip:** Always double-check the function form before solving, especially with shifted arguments like \( f(x+1) \).

Learn how to solve for f(3) when given f(x+1) = x^2 + 2x + 1. This problem explores key algebraic concepts such as function transformations and substitution. Suitable for high school students.

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