Final answer:
The fundamental period of the function f1(x) = sin(7x) cos(14x) is 2π/7, which is found by taking the least common multiple of the periods of sin(7x) and cos(14x). However, this answer is not among the provided options.
Step-by-step explanation:
The fundamental period of a trigonometric function like f1(x) = sin(7x) cos(14x) is the smallest positive value for which the function repeats its pattern. To find the fundamental period of f1(x), we have to find the fundamental periods of both sin(7x) and cos(14x) individually. The fundamental period of the sine and cosine functions is 2π. Therefore, for sin(7x), since the inside of the sine function is multiplied by 7, the period is 2π/7. Similarly, cos(14x) has a period of 2π/14, which simplifies to π/7. We then take the least common multiple (LCM) of these two periods to find the period of f1(x). The LCM of 2π/7 and π/7 is 2π/7, which is the period of f1(x). Thus, the fundamental period of f1(x) is 2π/7, which is not an option provided. All of the given options A) π, B) 2π, C) 4π, and D) π/2 do not coincide with the correct answer.