Bot GPT 4-o mini 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 \( x \).
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Start with the original 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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Now simplify \( (2x + 1)^2 \): \[ (2x + 1)^2 = 4x^2 + 4x + 1 \]
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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:
- 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 \( \boxed{34} \).
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