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Help with composite functions

How would I go about this problem?

Screenshot 2019-10-13 at 16.46.58.png

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.

IMG_3179.JPG

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

Thanks
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=4f(3) = ff(2) = (2)^2 + 2 = 4.

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

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


IMG_3179.JPG

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+2ff(1) = (2)^2 + 2 ??
Reply 3
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Yatayyat
OP
14
Original post by RDKGames
Hang on, why are you saying ff(1)=(2)2+2ff(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
Reply 4
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Yatayyat
OP
14
Original post by RDKGames
I suspect you have already found that f(3)=ff(2)=(2)2+2=4f(3) = ff(2) = (2)^2 + 2 = 4.

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

Similarly for fff(2)fff(2)

I don't understand why ff(2) = f(3)?
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)=...ff(x)=... and not f(x)=...f(x)=....

So f(2)=ff(1)=(1)2+2=3f(2) = ff(1) = (1)^2 + 2 = 3, but it doesnt say that f(2)=(2)2+2f(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.
Original post by Yatayyat
I don't understand why ff(2) = f(3)?


ff(2)=f(f(2))ff(2) = f(f(2))

but f(2)=3f(2) = 3,

so f(f(2))=f(3)f(f(2)) = f(3)
Reply 7
Avatar for Yatayyat
Yatayyat
OP
14
Original post by RDKGames
ff(2)=f(f(2))ff(2) = f(f(2))

but f(2)=3f(2) = 3,

so f(f(2))=f(3)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)

IMG_3180.JPG

So my answers to the Q are
f(3) =6
fff(1) = 6
fff(2) =11
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.
Reply 9
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Yatayyat
OP
14
Thank you once again :smile:

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