Which of the following correctly transforms f(x)=x2+9

Question

𝑓
(
𝑥
)
=
𝑥
2
+
9
to f(2x+1)
𝑓
(
2
𝑥
+
1
)
for x=2
𝑥
=
2
?(1 point)
Responses

34
34

25
25

14
14

26

Answer 1

To find \( f(2x + 1) \) when \( f(x) = x^2 + 9 \), we first need to substitute \( 2x + 1 \) into the function \( f \).

1. Start with \( f(x) = x^2 + 9 \).
2. Substitute \( 2x + 1 \) for \( x \) in \( f(x) \):

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

3. Expand \( (2x + 1)^2 \):

\[ (2x + 1)^2 = 4x^2 + 4x + 1 \]

4. Now substitute this back into the function:

\[ f(2x + 1) = 4x^2 + 4x + 1 + 9 = 4x^2 + 4x + 10 \]

5. Now plug in \( x = 2 \):

\[ f(2(2) + 1) = f(4 + 1) = f(5) \]

6. Calculate \( f(5) \):

\[ f(5) = 5^2 + 9 = 25 + 9 = 34 \]

So, the correct transformation of \( f(2x + 1) \) evaluated at \( x = 2 \) gives us \( 34 \).

The answer is:

34