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) = 1, f(n) =−f(n−1) for n ≥ 1 b) f(0) = 1, f(1) = 0, f(2) = 2, f(n) = 2f(n−3) for n ≥ 3 c) f(0) = 0, f(1) = 1, f(n) = 2f(n+1) for n ≥ 2 d) f(0) = 0, f(1) = 1, f(n) = 2f(n−1) for n ≥ 1 e) f(0) = 2,f(n) = f(n−1)ifnisoddandn ≥ 1and f(n) = 2f(n−2) if n ≥ 2

yes because they have the same amount of green and blur marbles.

step-by-step explanation:

0.02

step-by-step explanation:

time of 9 192 631 770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of the caesium 133 atom at 0 k (but other seconds are sometimes used in astronomy)

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph

vwhat effect does the word head have on the meaning of this passage?

a. it demonstrates how intelligent he was.

b. it shows he was a favorite of the teachers.

c. it indicates he would be a good preacher.

d. it reveals how self-important he was.

how does the choice of the word head contribute to the passage’s tone?

a. it offers a sense of entitlement.

step-by-step explanation: