l. a. Lct FU(z)]-F(w) and F-1 IF(w)] d note the Fourier transform of f(r) and inverse Fouricr transform of F()respectively. i. Show that the Fouricr transform is a lincar opcrator, that is, show that ii. Show that the inverse Fourier transform is a lincar operator; that is, show that b. If F(w) is the Fourier transform of f(x), show that the inverse Fouricr transform of eapF'(w) is f(z-β). Note: This result is known as the "shift theorem" for the Fourier transforms.