Let f(x) = 3x². What is f(-2x)?

Rationale

f(-2x) equals 12x².

To find f(-2x), we substitute -2x into the function f(x) = 3x², which results in f(-2x) = 3(-2x)² = 3(4x²) = 12x². This shows that the function evaluated at -2x yields a positive outcome due to the squaring of the negative input.

A (-36x²) YOUR ANSWER

This choice incorrectly applies the function by not squaring the input properly. Instead of obtaining a positive result, it suggests a negative outcome, which is impossible when squaring a term, as squaring any real number results in a non-negative value.

B (-12x²) YOUR ANSWER

Similar to choice A, this choice neglects the squaring of -2x and incorrectly introduces a negative factor. The function should yield a positive 12x² when calculated correctly, as the square of -2x is 4x², leading to a positive multiplication by 3.

C (-6x²) YOUR ANSWER

This option also miscalculates the square of -2x by providing a negative value. The correct calculation yields 12x², derived from properly squaring -2x and multiplying by 3. Thus, this option does not reflect the correct value.

D (12x²) CORRECT

This choice accurately represents the output of f(-2x) = 3(-2x)² = 12x². The squaring of -2x results in a positive value, and the multiplication with 3 confirms that this is the correct result.

E (36x²) YOUR ANSWER

This answer incorrectly assumes that the function multiplies the squared term by 9 instead of 3. The calculation of f(-2x) should result in 12x², not 36x², which indicates an error in applying the function.

Conclusion

Evaluating f(-2x) correctly reveals that it equals 12x². The process involves squaring the input and then multiplying by 3, reinforcing the function's property that all squared terms yield non-negative results. Choices A, B, C, and E fail to align with the correct calculations, illustrating common mistakes in function evaluation, while D stands as the valid outcome.