Need help finding g of f

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July 30th 2009, 10:51 PM
kro

{Solved} Need help finding g of f

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.
July 30th 2009, 11:49 PM
Swlabr

Quote:

Originally Posted by kro

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, $g \circ f = \{(1,1)(2,1)(3,a)(4,b)\}$ ( $(g \circ f)(x) = g(f(x))$ ). Can you see how to find $a$ and $b$ ?
July 31st 2009, 12:17 AM
kro

I think I got it?

Swlabr,
Here's what I have so please let me know if this is correct:
f(1)=3 so g(f(x))=1
f(2)=2 so g(f(x))=1
f(3)=4 so g(f(x))=2
f(4)=2 so g(f(x))=1

so......f of g = {(1,1),(2,1),(3,2),(4,1)}

Is this correct?
July 31st 2009, 12:30 AM
Swlabr

Quote:

Originally Posted by kro

Swlabr,
Here's what I have so please let me know if this is correct:
f(1)=3 so g(f(x))=1
f(2)=2 so g(f(x))=1
f(3)=4 so g(f(x))=2
f(4)=2 so g(f(x))=1

so......f of g = {(1,1),(2,1),(3,2),(4,1)}

Is this correct?

Yes, your numbers are correct. However, f of g is not g of f (in your last line you have written f of g not g of f).
July 31st 2009, 12:37 AM
kro

Thanks alot!

Ohhh yeah....I meant g of f.
Thanks alot for you help......FYI, I'm about to post another question that's kinda similar to this one except I have to find: f of f^-1