# If f={(-3,4),(-1,5),(-2,6),(2,4),(0,3)} and g={(4,3),(5,7),(3,0),(6,0)} then find set of ordered pair of gof and fog and represent in arrow diagram.?

May 29, 2018

$g \setminus \boldsymbol{o} \setminus f = \left\{\begin{matrix}- 3 & 3 \\ - 1 & 7 \\ - 2 & 0 - \\ 2 & 3 \\ 0 & 0\end{matrix}\right\}$

$f \setminus \boldsymbol{o} \setminus g = \left\{\begin{matrix}3 & 3 \\ 6 & 3\end{matrix}\right\}$

#### Explanation:

Given the specified ordered pairs, we can write the functions $f$ and $g$ by the mappings:

 f = { (-3, |-> 4), (-1, |-> 5), (-2, |-> 6), (2, |-> 4), (0, |-> 3) :} \ \ \ , and  g = { (4, |-> 3), (5, |-> 7), (3, |-> 0), (6, |-> 0) :}

We can construct:

$g \setminus \boldsymbol{o} \setminus f = g \left(f\right)$

 g \ bb(o) \ f = { (gf(-3)), (gf(-1)), (gf(-2)), (gf(2)), (gf(0)) :} = { (g(4)), (g(5)), (g(6)), (g(4)), (g(3)) :} = { (3), (7), (0), (3), (0) :}

Thus using an ordered pair representation, we have:

$g \setminus \boldsymbol{o} \setminus f = \left\{\begin{matrix}- 3 & 3 \\ - 1 & 7 \\ - 2 & 0 - \\ 2 & 3 \\ 0 & 0\end{matrix}\right\}$

However, We have a restricted domain for

$g \setminus \boldsymbol{o} \setminus f = g \left(f\right)$

We get:

 f \ bb(o) \ g = { (fg(4)), (fg(5)), (fg(3)), (fg(6)) :} = { (f(3)), (f(7)), (f(0)), (f(0)) :} = { ("undefined"), ("undefined"), (3), (3) :}

The domain of $f \circ g$ is that part of the domain of $g$ that yields a value in the domain of $f$.