Question 17

f(-2x) = 12x²

To find f(-2x), we substitute -2x into the function f(x) = 3x². This results in f(-2x) = 3(-2x)², which simplifies to 12x².

A) -36x²

This option is incorrect because it suggests that the output of the function is negative, while the calculation of f(-2x) results in a positive value. Additionally, the coefficient does not match the derived expression.

B) -12x²

This option is also incorrect as it reflects a negative outcome, which does not align with the function's evaluation. The correct calculation yields a positive result of 12x².

C) -6x²

This choice is incorrect since it does not represent the correct coefficient or sign. The function evaluation leads to a positive value, and thus this option does not match the outcome.

D) 12x²

This is the correct option. By substituting -2x into f(x) = 3x², we compute f(-2x) as 3(-2x)² = 3(4x²) = 12x², confirming that this is the correct answer.

E) 36x²

This option is incorrect, as it implies a different calculation that does not correspond to the evaluation of f(-2x). The correct output derived from the function is 12x², not 36x².

Conclusion

The correct answer is 12x² because it accurately represents the evaluation of f(-2x) using the provided function f(x) = 3x². All other options fail to reflect either the correct sign or the appropriate coefficient resulting from the calculation, confirming that option D is definitively correct.