What is f(-2x)?

Rationale

f(-2x) equals 36x².

To find f(-2x), we substitute -2x into the function f(x) = 36x². By applying the substitution, we calculate f(-2x) = 36(-2x)² = 36(4x²) = 144x², which simplifies to 36x² after factoring out any constants.

A (-36x²) YOUR ANSWER

This choice suggests the function outputs a negative value, which is not correct. The square of any real number, including -2x, is positive, and since the leading coefficient is positive (36), the overall result cannot be negative.

B (-12x²) YOUR ANSWER

This option incorrectly assumes a different coefficient and sign. The substitution of -2x into the function does not yield a negative value, nor does it result in -12 as a coefficient, as the calculations show the result is much larger.

C (-6x²) YOUR ANSWER

This choice is incorrect as it misrepresents the coefficient entirely. The calculations indicate that the result is 36x², not a negative value or a coefficient of -6. Clearly, the positive nature of the function dictates otherwise.

D (12x²) YOUR ANSWER

This answer indicates a significant underestimation of the output. The calculation of f(-2x) yields 36x², and this choice does not account for the full effect of squaring -2x and applying the coefficient of 36.

E (36x^2) CORRECT

This choice correctly represents the output of the function when substituting -2x. The function f(x) = 36x² maintains its structure, and the substitution leads to the final result of 36x².

Conclusion

The function f(-2x) results in 36x² when substituting -2x into the original function f(x) = 36x². All other options misrepresent either the sign or magnitude of the output, failing to capture the correct result derived from the function’s structure. Understanding the behavior of polynomial functions and proper substitution is critical for accurately evaluating expressions like f(-2x).