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Old 14th January 2012, 09:41 AM   #1 (permalink)
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Functions question.

hi all! i would like to ask a question regarding functions.

let inverse of a function be ' e.g. f '

they always ask u to draw f and f ' on the same graph,

but how about f 'f or ff ' ??

sometimes the f 'f and ff ' functions really become to complicated to form the eqn, cuz usually the power of X goes to 4 or more.

from my understanding, f 'f or ff ' is usually the line of symmetry, is it true? and if so, is it true for both? cuz when i tried to simplify f 'f or ff ' equations, i don't think the end result would be so simple...

and also the questions do not ask u to find f 'f or ff ' eqns before drawing.

please help! thanks so much! .

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Old 14th January 2012, 11:32 AM   #2 (permalink)
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Re: Functions question.

Originally Posted by blacktoast94 View Post
hi all! i would like to ask a question regarding functions.

let inverse of a function be ' e.g. f '

they always ask u to draw f and f ' on the same graph,

but how about f 'f or ff ' ??

sometimes the f 'f and ff ' functions really become to complicated to form the eqn, cuz usually the power of X goes to 4 or more.

from my understanding, f 'f or ff ' is usually the line of symmetry, is it true? and if so, is it true for both? cuz when i tried to simplify f 'f or ff ' equations, i don't think the end result would be so simple...

and also the questions do not ask u to find f 'f or ff ' eqns before drawing.

please help! thanks so much! .
it is only useful if you would to use f prime ff prime for sign chart purposes.
http://www.math.uncc.edu/~hbreiter/m...stinterval.pdf
using F prime, you test for the interval(s) which is/are continuous.

using f f prime, it is for you to see the inflection points which is in the shape of a curve ( this is when the points change in their course by trending up or down)

On a side note, i don't know why they only ask you draw f and f prime on the graph....apparently there is a need for these 3 elements to exist before you can draw a more accurate graph without your graphic calculator

If you use chain rule, the finding of the equation shouldn't be tough..That's unless you are finding it mixing with other methods..like quotient rule


If you want to reverse it...the integration part might a bit tough to do...multiple steps

anyways..i have not taken A maths or A level maths...this is from my 4 months calculus course in uni...i hope i didn't miss anything out for you...


Last edited by Crizzs; 14th January 2012 at 11:52 AM.
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Old 14th January 2012, 04:02 PM   #3 (permalink)
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Re: Functions question.

Originally Posted by blacktoast94 View Post
hi all! i would like to ask a question regarding functions.

let inverse of a function be ' e.g. f '

they always ask u to draw f and f ' on the same graph,

but how about f 'f or ff ' ??

sometimes the f 'f and ff ' functions really become to complicated to form the eqn, cuz usually the power of X goes to 4 or more.

from my understanding, f 'f or ff ' is usually the line of symmetry, is it true? and if so, is it true for both? cuz when i tried to simplify f 'f or ff ' equations, i don't think the end result would be so simple...

and also the questions do not ask u to find f 'f or ff ' eqns before drawing.

please help! thanks so much! .
f ' is normally used for derivative of the graph le....
So you now mean f ' is the inverse of a function.( shuld be written as f^-1)
Anywayz ff^-1 or in ur case ff ' or f 'f shuld be the graph y=x, which is the line of symmetry.(Note: i shall also use f ' as the inverse function)
Why is it y=x? It is based on the definition of the inverse of the function.
Meaning if f(a)=b then f '(b)=a
From f '(b) =a
=> ff '(b)=f(a) =b
So generally, ff '(x)=x. Hence it is y=x graph.
We can also argue the same way for f 'f(x) to get f 'f(x)=x

Also, please do note it is a composite function, so the domain follows the "inner" function.
i.e, domain of ff ' = domain of f '
and domain of f 'f = domain of f

Hope this helps


Last edited by megaman123; 14th January 2012 at 04:04 PM.
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Old 14th January 2012, 04:49 PM   #4 (permalink)
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Re: Functions question.

@megaman123: o.o so u mean f 'f or ff ' will confirm be Y=X?

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Old 14th January 2012, 04:55 PM   #5 (permalink)
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Re: Functions question.

wait... f ' is the differential of f or the inverse of f? lol im confused.
if f ' is the inverse of f (ie, f -1) then ff-1 is definitely y=x.

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Old 14th January 2012, 05:07 PM   #6 (permalink)
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Re: Functions question.

aforl:

f ' in the inverse of f haha

ok ff ' is definitely Y=X,

then how about f 'f?

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Old 14th January 2012, 05:23 PM   #7 (permalink)
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Re: Functions question.

Same!

10chars

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Old 14th January 2012, 07:43 PM   #8 (permalink)
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Re: Functions question.

A popular A level question would be to solve for f(x) = f^-1(x) (f inverse)
You don't have to go through all the trouble of finding the expression for f^-1, but rather recognize that
the line y=x, f(x) and f^-1(x) will all intersect at the same point, hence solving for f(x)=x would yield the required answer.

Hope this helps. Peace.

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Old 14th January 2012, 07:45 PM   #9 (permalink)
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Re: Functions question.

Originally Posted by blacktoast94 View Post
aforl:

f ' in the inverse of f haha

ok ff ' is definitely Y=X,

then how about f 'f?
You can draw reference from the properties of matrices you learnt in sec school.
Let the inverse of a matrix A be A^(-1)

Then A*A^(-1)=A^(-1)*A=I (the identity matrix).

Hope this helps. Peace.

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Old 14th January 2012, 09:23 PM   #10 (permalink)
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Re: Functions question.

Originally Posted by blacktoast94 View Post
@megaman123: o.o so u mean f 'f or ff ' will confirm be Y=X?
Yes in A levels this should be true.
And again, this y=x graph will have a domain, so be careful when you are asked to sketch it.

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