四、(10%) Suppose fc(ω) is cosine transform of (x) and is given by , please find the inverse transformf(x) of fc(ω). Hint: you may use the following definite integral:

(ㅡ)(8%) If the period of a set of periodic functions is 2π, what is the orthonormal basis of the vector space that these periodic functions belong to? You have to show the vectors in the basis are orthonormal to get full credit.