# Help with composite functions

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#1

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
0
1 year ago
#2
(Original post by Yatayyat)

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 .

Then for , note that this is just and you know what this is.

Similarly for 0
1 year ago
#3
(Original post by Yatayyat)

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 ??
0
#4
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
0
#5
I don't understand why ff(2) = f(3)?
0
1 year ago
#6
(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 and not .

So , but it doesnt say that .

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.
0
1 year ago
#7
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#8
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
0
1 year ago
#9
(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.
0
#10
Thank you once again 0
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