2. Assume we have two asymptotically non-negative functions f1(x),f2(x). Prove or disprove (a) max(f1(x),f2(x))=(f1(x)+f2(x)).(5 pt) (b) f1(x)+f2(x)=(min(f1(x),f2(x))). (5 pt) 3. Solve the following recurrences using method of substitution and find exact expressions for T(n) : (a) T(n)=T(n)+1,n=22k,T(2)=1(5pt) (b) T(n)=3T(n/2)+8n,n=2k,T(1)=1(5pt)