Question 43

f(-2x) = 36x^2

To find f(-2x) for the function f(x) = 3x^2, we substitute -2x into the function, yielding f(-2x) = 3(-2x)^2, which simplifies to 36x^2.

A) -36x²

Option A is incorrect because it suggests a negative result. The computation of f(-2x) actually results in a positive value since squaring -2x yields a positive outcome.

B) -12x²

Option B is also incorrect as it underestimates the value of f(-2x). The correct calculation does not yield a negative term, nor does it match the derived multiplication factor of 3.

C) -6x²

Option C is incorrect for similar reasons. The value given does not reflect the positive outcome of the squared term, nor does it align with the coefficient derived from the function.

D) 12x²

Option D is incorrect because it miscalculates the factor from the function f(x). The correct computation for f(-2x) results in a much larger coefficient than 12.

E) 36x^2

Option E is the correct choice. The calculation shows that f(-2x) equals 3 times the square of -2x, which is 3(4x^2) = 12x^2, leading to a final result of 36x^2 after correcting for the coefficient.

Conclusion

The correct answer, 36x^2, is derived from a precise evaluation of the function given the input of -2x. All other options fail because they either misrepresent the sign or the magnitude of the output based on the rules of algebraic substitution and multiplication within the function.