1. Let x[n] be a signal with x[n] = 0 for n<-1 and n > 3. For each signal given below, determine the values of n for which it is guaranteed to be zero. (a) x [n -2] (b) x [n+ 3] (c) x [-n + 1]

Answer:a) n<1 and n>5b)  0 < n < -4c)  n > 2 and n < -2Step-by-step explanation:The signal is given by x[n] = 0 for n < -1 and n > 3The problem asks us to determine the values of n for which it's guaranteed to be zero.a) x[n-2]We know that n -2 must be less than -1 or greater than 3.Therefore we're going to write down our inequalities and solve for n[tex]n-2<-1\\n<-1+2\\n<1\\\\n-2>3\\n>5[/tex]Therefore for n<1 and n>5 x [n-2] will be zerob) x [n+ 3] Similarly, n + 3 must be less than -1 or greater than 3[tex]n+3<-1\\n<-1-3\\n<-4\\\\n+3>3\\n>3-3\\n>0[/tex]Therefore for n< -4 and n>0, in other words, for 0 < n < -4  x[n-2] will be zeroc)x [-n + 1]Similarly, -n+1 must be less than -1 or greater than 3[tex]-n+1<-1\\-n<-1-1\\-n<-2\\n>2\\\\-n+1>3\\-n>3-1\\-n>2\\n<-2[/tex]Therefore, for n > 2 and n < -2  x[-n+1] will be zero