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

Question

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

14
14

26
26

25
25

34

Answer 1

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