Let $f:\{3,9,12\} \rightarrow\{1,3,4\}$ and $g:\{1,3,4,5\} \rightarrow\{3,9\}$ be
defined as $f=\{(3,1),(9,3),(12,4)\}$ and
$g=\{(1,3),(3,3),(4,9),(5,9)\}$
Find (i) (g off) (ii) (f o g).
(i) g o f
To find: g o f
Formula used: g o f = g(f(x))
Given: f = {(3, 1), (9, 3), (12, 4)} and g = {(1, 3), (3, 3),(4, 9), (5, 9)}
Solution: We have,
$g \circ f(3)=g(f(3))=g(1)=3$
$g \circ f(9)=g(f(9))=g(3)=3$
$g \circ f(12)=g(f(12))=g(4)=9$
Ans) g o f = {(3, 3), (9, 3), (12, 9)}
(ii) f o g
To find: f o g
Formula used: f o g = f(g(x))
Given: $f=\{(3,1),(9,3),(12,4)\}$ and $g=\{(1,3),(3,3),(4,9),(5,9)\}$
Solution: We have,
fog(1) = f(g(1)) = f(3) = 1
fog(3) = f(g(3)) = f(3) = 1
fog(4) = f(g(4)) = f(9) = 3
fog(5) = f(g(5)) = f(9) = 3
Ans) f o g = {(1, 1), (3, 1), (4, 3), (5, 3)}