Question

Let $\mathrm{S}=\{-1,0,2,4.7\}$. Find f(S) if

1. role="math" localid="1668419106110" $f\left(x\right)=1$
2. role="math" localid="1668419096298" $f\left(x\right)=2+1$
   
3. role="math" localid="1668419089300" $f\left(x\right)=[x/5]$
   
4. $f\left(x\right)=[\left(x^2+1\right)/3]$
   

Short answer

1. $f\left(S\right)=\{-1,0,2,4,7\}$
   
2. $f\left(S\right)=\{-115915]$
   
3. localid="1668419770708" $f\left(\mathrm{S}\right)=\{0,1\}$
   
4. $f\left(\mathrm{S}\right)=\{0,1,5,1,6\}$
   

Step-by-step solution

Step: 1

Given$\mathrm{S}=\{-1,0,2,4,7\}$

a. f(x) = 1

Then$f\left(S\right)=\{-1,0,2,4,7\}$

Step: 2

b. $f\left(x\right)=2x+1$

If x = - 1 then f(x) = - 1

If x = 0 then f(x) = 0

If x = 2 then f(x) = 2

If x = 4 then f(x) = 4

If x = 7 then f(x) = 7

Then$f\left(S\right)=\{-1,1,5,9,1,5\}$

Step: 3

c.$f\left(x\right)=[x/5]$

If x = - 1 then f(x) = 0

If x = 0 then f(x) = 0

If x = 2 then f(x) = 0

If x = 4 then f(x) = 0

If x = 7 then f(x) = 1

Then$f\left(\mathrm{S}\right)=\{0,1\}$

Step: 4

d. $f\left(x\right)=[\left(x^2+1\right)/3]$

If x = - 1, then f(x) = 0

If x = 0, then f(x) = 0

If x = 2, then f(x) = 1

If x = 4, then f(x) = 5

If x = 7, then f(x) = 16

Then $f\left(\mathrm{S}\right)=\{0,1,5,1,6\}$