Let f = {(1, 2), (3, 5), (4, 1)) and g = {(2, 3), (5, 1), (1, 3)}.

Question:

Let f = {(1, 2), (3, 5), (4, 1)) and g = {(2, 3), (5, 1), (1, 3)}. Then, gof = __________ and fog = __________.

Solution:

Given: f = {(1, 2), (3, 5), (4, 1)) and g = {(2, 3), (5, 1), (1, 3)}

$f o g(x)=f(g(x))$

$f o g(1)=f(g(1))$

$=f(3)$

$=5$

$f o g(2)=f(g(2))$

$=f(3)$

$=5$

$f o g(5)=f(g(5))$

$=f(1)$

$=2$

Hence, $f o g=\{(1,5),(2,5),(5,2)\}$

$g o f(x)=g(f(x))$

$g o f(1)=g(f(1))$

$=g(2)$

$=3$

$g o f(3)=g(f(3))$

$=g(5)$

$=1$

$g o f(4)=g(f(4))$\

$=g(1)$

$=3$

Hence, $g \circ f=\{(1,3),(3,1),(4,3)\}$

Hence, gof $=\{(1,3),(3,1),(4,3)\}$ and fog $=\{(1,5),(2,5),(5,2)\}$.

 

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