NO1 and NO3

1Find /(1)/(2), / (3), and f (4) if f(n) is defined reur. 5. Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f(n) when n is a nonnegative integer and prove that your formula is valid a) f(0) 0, f (n) 2f(n -2) for n 2 1 sively by f(0)-1 and for n -0,1,2,.. b) f(n+1) 3f(n) e) f(n + 1) = 2/u). 2. Find f(1), f(2). f (3), f (4), and f(5) if f (n) is defined e) (0)-2, f(1) 3,f(n)(n-1)-1 for recursively by f(0) 3 and for n 0, 1,2,... a) f(n +1)-2f (n). b) f(n +1) 3f(n) +7. c) fn +1(n2 -2f(n) 2. ne 2 e) f (0) = I, f(n) = 3/(n-1) if n is odd and n 21 and f(n)9f (n-2) if n is even and n 2 2 3. Find f (2), f (3). f(4), and f(5) if f is defined recur 6. Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f(n) when n is a nonnegative integer and prove that your formula is valid sively by f (0) -1, 1)s 2, and for n 1.2, . . . b) f(n + 1) = f(n)2f(n-1) 4. lind (2), (3), (4), and /(5) if f is delined recur- sively by f(()-f( 1 ) = 1 and for n = 1 , 2, . . . a) f(n + 1) = f(n)-f(n-1). for n 3 e) f (0) 0, f (l) l, f (n) 2/(n + 1) for n > 2 d) f(0)=0,/U)= I. f(n) = 2/(-1) for n >1 e) fo) 2.n)F Iyifn is odd and n I and