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Question 367753: Composition of Functions problem:
r(t)=q(p(t))
Given:
t | p(t) | q(t) | r(t)
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0 | 4 | ?? | ??
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1 | ?? | 2 | 1
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2 | ?? | ?? | 0
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3 | 2 | 0 | 4
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4 | 1 | 5 | ??
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5 | 0 | 1 | 3
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Fill in ?? with correct answer. I need help with a process to solve this problem.
I can solve r(0)=?? by this method: r(0)=q(p(0)) knowing that r(0) will be equal to q(p(0)), then r(0)=q(4) because I find that p(0) is equal to 4 which becomes q(4), next I see that q(4) is equal to 5, therefore r(0)=5.
I am having difficulty with a process to find for p(t) and q(t).
Any ideas?
Thanks,
Deb
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Composition of Functions problem:
r(t)=q(p(t))
Given:
t | p(t) | q(t) | r(t)
-----------------------------
0 | 4 | ?? | ??...........r(0)= q(p(0))=q(4)= 5
..........................q(0) =q[p(5)] = r(5) = 3
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1 | ?? | 2 | 1..........................p(1) = q^-1(r(1))= q^-1(1) = 5
-----------------------------
2 | ?? | ?? | 0...........p(2) = q^-1(r(2)) = q^-1(0)= 3
..........................q(2) = p^-1(r(2)) = p^-1(0) = 5
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3 | 2 | 0 | 4
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4 | 1 | 5 | ??................r(4) = q(p(4)) = q(1)=2
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5 | 0 | 1 | 3
-----------------------------
Fill in ?? with correct answer. I need help with a process to solve this problem.
I can solve r(0)=?? by this method: r(0)=q(p(0)) knowing that r(0) will be equal to q(p(0)), then r(0)=q(4) because I find that p(0) is equal to 4 which becomes q(4), next I see that q(4) is equal to 5, therefore r(0)=5.
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Cheers,
Stan H.
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