What is the result of \(f(2)\) if \(f(x) = x^2 + 2x + 1\)?

To find the value of (f(2)) for the function (f(x) = x^2 + 2x + 1), we will substitute (2) for (x) in the function:

1. Start with the function:

[

f(x) = x^2 + 2x + 1

]

2. Substitute (x) with (2):

[

f(2) = (2)^2 + 2(2) + 1

]

3. Perform the calculations step-by-step:

• First, calculate ((2)^2):

[

(2)^2 = 4

]

• Next, calculate (2(2)):

[

2(2) = 4

]

4. Now, combine these results with the constant (1):

[

f(2) = 4 + 4 + 1

]

5. Add the numbers together:

[

4 + 4 = 8

]

[

8 + 1 = 9