Q16) Consider the function f(x) = 2x, 0

Q16) Consider the function f(x) = '2x, 0 < a: < 1. Let feven@) be the even extension of f to the interval 1 < a: < 1. Let fodd(x) be the odd extension of f to the interval 1 < a: < 1. Then f ( even and Suppose we wanted to use the first couple of terms of a Fourier series to approximate f in the Which would give the best representation? Answer: 1. Use the Fourier representation of f(x), extended as a periodic function with -F 1) f(x). 2. Use the Fourier cosine series for the even extension even. 3. Use the Fourier sine series for the odd extension fodd. 4. Use the Fourier sine series for the even extension fe 5. Any of the above choices would be equally suitable.