Answer
a)f(S) = { 1 }
b)f(S) = {-1, 1, 5, 9, 15}
c)f(S) = {0, 1, 2}
d)f(S) = {0, 1, 5, 16}
Work Step by Step
a)
the function was ƒ(x) = 1
it is a constant function not dependent on variable value so for every value from set S the ans remains the same.
f(S) = { 1 }
b)
the function was ƒ(x) = 2x + 1
for every value from set S and put in the function ƒ(x) we get some answers that are written correspondingly as ordered pairs,
f = {(-1, -1), (0, 1), (2, 5), (4, 9), (7, 15)}
here for first ordered pair (-1,-1) first value (-1) is the value taken from set S and putted in the function as
ƒ(-1) = 2(-1) + 1=-1 which is the ans and written in 2nd of the ordered pair
similarly, (0, 1) when we put x=0 in function as
ƒ(0) = 2(0) + 1=1
hence in the same way for all values of S we get a set of answers as f(S) = {-1, 1, 5, 9, 15}
c)ƒ(x) = ⌈x/5⌉
for every value from set S and put in the function ƒ(x) we get some answers that are written correspondingly as ordered pairs,
f = {(-1, 0), (0, 0), (2, 1), (4, 1), (7, 2)}
for ordered pair (-1,0) -1 is the value of x from S and 0 is the answer by putting x=-1 in function
similar for all values of S we get as set of answers as
f(S) = {0, 1, 2}
d)ƒ(x) = ⌊(x2+ 1)/3⌋
for every value from set S and put in the function ƒ(x) we get some answers that are written correspondingly as ordered pairs,
f = {(-1, 0), (0, 0), (2, 1), (4, 5), (7, 16)}
for ordered pair (-1,0) -1 is the value of x from S and 0 is the answer by putting x=-1 in function
similar for all values of S we get as set of answers as
f(S) = {0, 1, 5, 16}
