Question

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4. Let A- (0,1,2,3,4) and f:A and f(f(n)) A where f(n) 2n mod 5. Construct a table with values for n, f(n)

Answer 1

Answer:

The required table is shown below.

Step-by-step explanation:

The given set is

$A=\{0,1,2,3,4\}$

It is given that

$f:A\rightarrow A$

where, $f(n)=2n(mod 5)$.

We need to construct a table with values for n, f(n) and f(f(n)).

The elements of set are 0,1,2,3 and 4 so these are the values of n.

At n=0,

$f(0)=2(0)(mod 5)=0(mod 5)=0$

$f(f(0))=f(0)=0$

At n=1,

$f(1)=2(1)(mod 5)=2(mod 5)=2$

$f(f(1))=f(2)=2(2)(mod 5)=4(mod 5)=4$

At n=2,

$f(2)=2(2)(mod 5)=4(mod 5)=4$

$f(f(2))=f(4)=3$

At n=3,

$f(3)=2(3)(mod 5)=6(mod 5)=1$

$f(f(3))=f(1)=2$

At n=4,

$f(4)=2(4)(mod 5)=8(mod 5)=3$

$f(f(4))=f(3)=1$

Therefore the required table is

n              f(n)               f(f(n))

0               0                 0

1                2                 4

2               4                 3

3                1                 2

4               3                 1