Question

Which of the following correctly transforms f(x)=x^2 +9 to f(2x+1) for x=2 ?(1 point) Responses 26 26 14 14 25 25 34

Answer 1

To find \( f(2x + 1) \) for the function \( f(x) = x^2 + 9 \), we'll first substitute \( 2x + 1 \) into the function and then evaluate it at \( x = 2 \).

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

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

3. Expand \( (2x + 1)^2 \):
\[
(2x + 1)^2 = 4x^2 + 4x + 1
\]
Therefore:
\[
f(2x + 1) = 4x^2 + 4x + 1 + 9 = 4x^2 + 4x + 10
\]

4. Now evaluate \( f(2x + 1) \) at \( x = 2 \):
\[
f(2(2) + 1) = f(4 + 1) = f(5)
\]

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

Thus, the correct transformation evaluated at \( x = 2 \) yields \( 34 \).

The answer is **34**.