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