Question

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

Answer 1

To transform the function \( f(x) = x^2 + 9 \) to \( f(2x+1) \), we need to substitute \( 2x + 1 \) into the function in place of \( x \).

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

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

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

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

Next, we need to find \( f(2) \), so substitute \( x = 2 \) into the equation we just found:

5. Calculate \( f(2) \):
\[
f(2) = 4(2)^2 + 4(2) + 10
\]
\[
= 4 \cdot 4 + 8 + 10
\]
\[
= 16 + 8 + 10
\]
\[
= 34
\]

Therefore, the correct transformation gives us \( f(2) = 34 \).

The answer is \( \boxed{34} \).