Question

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

Responses

34

14

25

26

Answer 1

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

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

Now, substitute \( 2x + 1 \) for \( x \):
\[
f(2x + 1) = (2x + 1)^2 + 9
\]

Next, expand \( (2x + 1)^2 \):
\[
(2x + 1)^2 = 4x^2 + 4x + 1
\]

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

Now, we need to evaluate \( f(2 \cdot 2 + 1) = f(4 + 1) = f(5) \):
\[
f(5) = 5^2 + 9 = 25 + 9 = 34
\]

Thus, the correct transformation when \( x = 2 \) is:
**34**