Yatayyat
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How would I go about this problem?

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I have worked out what ff(1) and ff(2) to be but can't see how this would help me with working out f(f(f(x))) at the values x=1 and x=2.

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Is there some sort of pattern that I'm missing when finding out what f(3) is to be?

Thanks
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RDKGames
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(Original post by Yatayyat)
How would I go about this problem?

I have worked out what ff(1) and ff(2) to be but can't see how this would help me with working out f(f(f(x))) at the values x=1 and x=2.

Is there some sort of pattern that I'm missing when finding out what f(3) is to be?

Thanks
I suspect you have already found that f(3) = ff(2) = (2)^2 + 2 = 4.

Then for fff(1), note that this is just ff(2) and you know what this is.

Similarly for fff(2)
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RDKGames
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(Original post by Yatayyat)

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Is there some sort of pattern that I'm missing when finding out what f(3) is to be?
Hang on, why are you saying ff(1) = (2)^2 + 2 ??
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Yatayyat
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(Original post by RDKGames)
Hang on, why are you saying ff(1) = (2)^2 + 2 ??
If ff(x) = x^2 +1 and f(1) = 2

then ff(1) = (2)^2 + 2 = 6 , is this incorrect?

If so then I'm guessing I should've subbed in x=1 and not x =2

so correct ff(1) = (1)^2 + 2 =3

and ff(2) = (2)^2 + 2 = 6
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Yatayyat
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(Original post by RDKGames)
I suspect you have already found that f(3) = ff(2) = (2)^2 + 2 = 4.

Then for fff(1), note that this is just ff(2) and you know what this is.

Similarly for fff(2)
I don't understand why ff(2) = f(3)?
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RDKGames
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(Original post by Yatayyat)
If ff(x) = x^2 +1 and f(1) = 2

then ff(1) = (2)^2 + 2 = 6 , is this incorrect?
Yes. The function is defined by ff(x)=... and not f(x)=....

So f(2) = ff(1) = (1)^2 + 2 = 3, but it doesnt say that f(2) = (2)^2 + 2.

If so then I'm guessing I should've subbed in x=1 and not x =2

so correct ff(1) = (1)^2 + 2 =3

and ff(2) = (2)^2 + 2 = 6
This is now correct.
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RDKGames
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(Original post by Yatayyat)
I don't understand why ff(2) = f(3)?
ff(2) = f(f(2))

but f(2) = 3,

so f(f(2)) = f(3)
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Yatayyat
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(Original post by RDKGames)
ff(2) = f(f(2))

but f(2) = 3,

so f(f(2)) = f(3)
Yes thank you, it makes sense to me now
so therefore I know fff(1) = ff(2) and fff(2) = ff(3)

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So my answers to the Q are
f(3) =6
fff(1) = 6
fff(2) =11
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RDKGames
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(Original post by Yatayyat)
Yes thank you, it makes sense to me now
so therefore I know fff(1) = ff(2) and fff(2) = ff(3)

So my answers to the Q are
f(3) =6
fff(1) = 6
fff(2) =11
Yep.
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Yatayyat
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#10
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Thank you once again
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