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

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

25
25

14
14

34
34

26

1 answer

To transform the function \( f(x) = x^2 + 9 \) to \( f(2x + 1) \) and then evaluate it at \( x = 2 \), follow these steps:

  1. Substitute \( 2x + 1 \) in place of \( x \) in the function \( f(x) \):

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

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

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

So we have:

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

  1. Now, evaluate \( f(2x + 1) \) at \( x = 2 \):

\[ f(2(2) + 1) = f(5) = 4(2^2) + 4(2) + 10 \]

Calculating that:

\[ f(5) = 4(4) + 8 + 10 = 16 + 8 + 10 = 34 \]

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

The correct response is 34.