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d) 3f(x)−2g(x), in which f(x) and g(x) are the functions given in a) and b), respectively; e) g′(x), in which g(x) is the function given in b);
Find the Fourier Transform of the following functions and confirm that in each case the Fourier Transform vanishes as ω→±∞ : a) f(x)={10​ if −a≤x≤a otherwise ​,a>0; b) g(x)=a2+x21​,a>0 hint: ∫−∞∞​a2+x2cosωx​dx=aπ​e−a∣ω∣ c) p(x)={eiax0​ if 0<x<1 otherwise ​