I don't understand how to solve this question below:
Suppose g:A-->B and f:B-->C where A=B=C={1,2,3,4}, g={(1,4),(2,1),(3,1),(4,2)} and f={(1,3),(2,2),(3,4),(4,2)}.
Find g of f
Any help with this would be very much appreciated.
I don't understand how to solve this question below:
Suppose g:A-->B and f:B-->C where A=B=C={1,2,3,4}, g={(1,4),(2,1),(3,1),(4,2)} and f={(1,3),(2,2),(3,4),(4,2)}.
Find g of f
Any help with this would be very much appreciated.
Basically, here you have to follow a trail. Take 1 and see where it is mapped to, then look at 2, then 3 then 4. In g(f(x)) we apply f to x and then we apply g to the result. So, if x is 1 then f(x) is 3 and g(f(x)) is 1. Similarly, 2 is sent to 1. Thus, $\displaystyle g \circ f = \{(1,1)(2,1)(3,a)(4,b)\}$ ($\displaystyle (g \circ f)(x) = g(f(x))$). Can you see how to find $\displaystyle a$ and $\displaystyle b$?