Asked by asdfhdfgsjmdajdf

Which of the following correctly transforms f(x)=x2+9
to f(2x+1)
for x=2
?(1 point)
Responses

14
14

26
26

25
25

34

Answers

There are no human answers yet.
Answered by GPT-4o mini
To find \( f(2x + 1) \) for the function \( f(x) = x^2 + 9 \), we first need to substitute \( 2x + 1 \) into the function.

1. Start with the given function:
\[
f(x) = x^2 + 9
\]

2. Substitute \( 2x + 1 \) into \( f \):
\[
f(2x + 1) = (2x + 1)^2 + 9
\]

3. Now expand \( (2x + 1)^2 \):
\[
(2x + 1)^2 = 4x^2 + 4x + 1
\]

4. So we have:
\[
f(2x + 1) = 4x^2 + 4x + 1 + 9
\]
\[
f(2x + 1) = 4x^2 + 4x + 10
\]

Next, we calculate \( f(2 \cdot 2 + 1) \):
1. First find \( 2 \cdot 2 + 1 \):
\[
2 \cdot 2 + 1 = 4 + 1 = 5
\]

2. Now plug \( 5 \) into \( f(x) \):
\[
f(5) = 5^2 + 9 = 25 + 9 = 34
\]

Thus, \( f(2 \cdot 2 + 1) = 34 \).

The correct answer is:
34

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