Question

Let S = {−1, 0, 2, 4, 7}. Find f (S) if
a) f (x) = 1.
b) f (x) = 2x + 1.
c) f (x) = x /5.
d) f (x)=(x2 + 1)/3

Answer 1

S = { -1, 0, 2, 4 ,7 }

a)  f(S) = { 1}      as all elements in the domain map to the same element.
                             f is a constant function.
b) f(S) = set of all the real values obtained by calculating 2 * x + 1, where
                  x belongs to S.
            =    { -1, 1, 5, 9, 15 }
c) f(S) =  { -1/5,  0, 2/5 , 4/5 , 7/5 }

d)  f(S) =  {  (1²+1)/3 = 2/3,  1/3,  5/3, 17/3 ,  50/3 }

Answer 2

1.  f(x) = 1 is a constant function and hence its value will remain the same for all points.

2.  f(x) = 2x+1 for S = {-1,0,2,4,7)
 f(-1) =2*(-1)+1 = -1
 f(0)  =2*(0)+1 = 1
f(2) = 2*2+1 = 5
f(4) = 2*4+1 = 9
f(7) = 2*7+1 15

3. f(x)=x/5
f(-1) = -1/5
 f(0)  = 0/5=0
f(2) = 2/5
f(4) = 4/5
f(7) = 7/5

4. f (x)=(x2 + 1)/3
f(-1) = 2/3
 f(0)  = 1/3
f(2) = 5/3
f(4) = 17/3
f(7) = 50/3