Inverse Functions (1 Viewer)

[TrueHappiness]

f(x) = 1/6 (x^2 - 4x + 24)

f(x) has domain and range
x>=2 and y>= 10/3 to acquire large inverse function with positive no.

If N is negative real no. what is

f-1(f(N)) where f-1(x) is inverse of f(x)

 

[random-1006]

f(x) = 1/6 (x^2 - 4x + 24)

f(x) has domain and range
x>=2 and y>= 10/3 to acquire large inverse function with positive no.

If N is negative real no. what is

f-1(f(N)) where f-1(x) is inverse of f(x)

doesnt make much sense, but ill see what i can do

It would be unknown

the inverse function can only give out values that are in the range of the original function

now range of the original function is y>= 10/3 ( ie positive y)

f^ -1 ( f(N) ) would equal N if N >= 10/3

otherwise we do not know what it may equal

 

[jet]

doesnt make much sense, but ill see what i can do

It would be unknown

the inverse function can only give out values that are in the range of the original function

now range of the original function is y>= 10/3 ( ie positive y)

f^ -1 ( f(N) ) would equal N if N >= 10/3

otherwise we do not know what it may equal

It's not "unknown", we say that expression is "undefined". Given the function is only defined for x ≥ 2, then f(N) is undefined given N < 0. You don't even need to worry about the inverse since the original function is undefined for the value of N specified.

 

[random-1006]

It's not "unknown", we say that expression is "undefined". Given the function is only defined for x ≥ 2, then f(N) is undefined given N < 0. You don't even need to worry about the inverse since the original function is undefined for the value of N specified.

sorry for not having a bullet proof uni answer, unknown , undefined, pretty much same thing lol

i spent an hour yesterday and an hour today in algebra lecturers going through proofs that vector x + vector y = vector y + vector x

and that vector x + ( - vector x) =0

i understand that sometimes math needs rigor, but most of the time it is useless, besides that would be perfectly acceptable as an hsc answer

 

[random-1006]

The BOS makes a distinction between unknown and undefined.

i will bet you , say , $5000, a question of that nature will not come up in an hsc ( not in say the next 20years papers)

and if it did come up they would accept "unknown" as a correct answer. all they are looking for is that someone doesnt say "N", but the very way that question is asked pretty much ensures that it will never be an hsc question.

that is little nitty gritty uni detail, for an hsc they wouldnt give a shit

 

[random-1006]

I do not see why you wouldn't just learn that 'undefined' is a mathematical term, the same way 'induction' is a mathematical term...

It's not a uni detail, it's in HSC textbooks.

i know its a math term u noob, but you are not going to lose a mark on an hsc paper because of it, and no one would set a question like the one given in an exam

 

[random-1006]

actually, according to my maths teachers, you can.

well hes a noob just like you

do you honestly think a question like that would be in the exam

the most common test of that content would be find absolute value of arcsin ( sin ( 5pi/3) ) , not some stupid trick question that really has no clear cut answer, defined and "unknown". Well , do you know what it would equal??. No, hence its unknown. your A NOOBCAKE

 

[random-1006]

oi noob, do u think that they will ever ask a question similar ( same words , different function) on a hsc.

if not, shut the fuck up

 

[TrueHappiness]

the answer is actually 4 - N. I think it has smting to do with symmetry.

 

[life92]

f(x) = 1/6 (x^2 - 4x + 24)

f(x) has domain and range
x>=2 and y>= 10/3 to acquire large inverse function with positive no.

If N is negative real no. what is

f-1(f(N)) where f-1(x) is inverse of f(x)

f(x) = 1/6 (x^2 - 4x + 24)
= 1/6 ((x-2)^2+20)

which means the vertex is (2, 10/3) and the axis of symmetry is x=2

Consider some z that exists in the restricted domain of f(x) and then N which doesn't belong to that domain, where f(z)=f(N).
Now, by symmetry, (z+N)/2 = 2, since the axis of symmetry is x=2.
=> z=4-N
Now, f-1(f(N))=f-1(f(z)), since f(N)=f(z), and therefore f-1(f(N))=f-1(f(4-N))=4-N since 4-N belongs to the restricted domain of f(x).

Hopefully that makes sense

 

[shaon0]

Actually, according to my maths teachers, you can.

I commend your self-restraint...answer's 4-N, theres a past HSC 3u q like this.

EDIT:Answered