Solve this

Solution:

(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)}