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 \( x = 2 \).
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Start with the function: \[ f(x) = x^2 + 9 \]
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Substitute \( 2x + 1 \) into the function: \[ f(2x + 1) = (2x + 1)^2 + 9 \]
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Expand \( (2x + 1)^2 \): \[ (2x + 1)^2 = 4x^2 + 4x + 1 \] Therefore: \[ f(2x + 1) = 4x^2 + 4x + 1 + 9 = 4x^2 + 4x + 10 \]
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Now evaluate \( f(2x + 1) \) at \( x = 2 \): \[ f(2(2) + 1) = f(4 + 1) = f(5) \]
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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.