VCE Methods Question Thread!

[psyxwar]

When you take the inverse of a many-to-one function, you get a one-to-many relation, which is no longer a function (well, not by the definition VCE methods goes by). If you want an inverse function to exist, then the original function must be a one-to-one. x^2 and x^4 are many-to-one functions so if you want an inverse function to exist you need to restrict its domain so it's a one-to-one function.

[IndefatigableLover]

When you take the inverse of a many-to-one function, you get a one-to-many relation, which is no longer a function (well, not by the definition VCE methods goes by). If you want an inverse function to exist, then the original function must be a one-to-one. x^2 and x^4 are many-to-one functions so if you want an inverse function to exist you need to restrict its domain so it's a one-to-one function.

^If you want further reading on this then check out this: http://www.purplemath.com/modules/invrsfcn2.htm

[Zues]

so basically anything can have an inverse, but for a inverse of a function, f(x) needs to be one to one?

[pi]

so basically anything can have an inverse, but for a inverse of a function, f(x) needs to be one to one?

Yes.

[Zues]

Yes.

i remember just doing multiplication all day in grade 2 :/

when will we need inverses in life?

[SE_JM]

So, if the question asked you,
Find the inverse of x², then the answer could be + or - x^1/2

But if the question asked you,

Find the inverse function of x², then the answer only can be x^1/2 ?

[pi]

when will we need inverses in life?

Depends on your life! I don't need them in my life

So, if the question asked you,
Find the inverse of x², then the answer could be + or - x^1/2

But if the question asked you,

Find the inverse function of x², then the answer only can be x^1/2 ?

Not quite, you need to actually show the restricted domain of the inverse function in your answer. eg. would be notation I'd use.

[SE_JM]

Thanks!

Could I  ask one more question?

Regarding the very first question i asked: Finding inverse of x² and x⁴,

Since the question doesn't explicitly say find the inverse function, does that mean my answer is right? (as + - x^1/2 and + - x^1/4)?

Thank you

[Zues]

if i had f(x) = x / 2, i know that f(x) is its own inverse. But a question asks what are the points of intersection, why is there none, as apossed to my "infinite" ?

[keltingmeith]

(okay, I shouldn't actually be here and have work to do, buuuuuut you guys got me interested in some things, so... If I return after this, can people please tell me to get lost? kthx <3)

When you take the inverse of a many-to-one function, you get a one-to-many relation, which is no longer a function (well, not by the definition VCE methods goes by).

Pray tell what the other definition of a function in mathematics is?

i remember just doing multiplication all day in grade 2 :/

when will we need inverses in life?

The thing with high school mathematics is that a lot of this isn't required for life - it IS, however, required for future mathematics, which may lend itself to some career you do (particularly if you go for anything in the sciences or engineering, plus other stats-heavy careers such as things contained by commerce degrees).

In particular, this is useful for defining the inverse circular functions (done in specialist~), which are INCREDIBLY useful for finding the angles defined by triangles.

The idea of the "inverse function" is also particularly useful in defining the logarithm, which is the inverse of the exponential function. In fact, this definition has MANY applications in scientific modelling by differential equations (an example being the break-down of radioactive isotopes). Whilst the inverse function itself didn't help us with these models, the knowledge it gave us has.

[Zues]

final question.

a question in the book says find the inverse function of f(x) = x^2 −6x+3, after our discussions i would say there is no inverse function since it is not one to one.

however derrick ha's book has a similar question, f(x) = x^2 +5x + 3, and what he does is swap x and y, then transform it into TP form, then re arranges for y which results in a = +- , then he says because it asks for an inverse function you go f^-1(x) = - .... or f^-1(x) = + ....

[pi]

Our discussions actually suggested that many-to-one functions DO have inverse functions when you actively apply appropriate domain restrictions. Personally I wouldn't write f^-1(x) = - .... or f^-1(x) = + .... UNLESS I had written the domains and shown this in my working acknowledging I'd made f into two one to one functions first.

[alchemy]

I plugged in the equation of an circle on the cas. Tried to find the maximum point. It says select graph and I tried to select it. But it won't select >.<
How do I find the maximum or minimum points?

[pi]

Why do you need a CAS for that? Y coordinate of centre plus radius!

[Zues]

Our discussions actually suggested that many-to-one functions DO have inverse functions when you actively apply appropriate domain restrictions. Personally I wouldn't write f^-1(x) = - .... or f^-1(x) = + .... UNLESS I had written the domains and shown this in my working acknowledging I'd made f into two one to one functions first.

what do you mean? if you have an example as well?

final question.

a question in the book says find the inverse function of f(x) = x^2 −6x+3, after our discussions i would say there is no inverse function since it is not one to one.

however derrick ha's book has a similar question, f(x) = x^2 +5x + 3, and what he does is swap x and y, then transform it into TP form, then re arranges for y which results in a = +- , then he says because it asks for an inverse function you go f^-1(x) = - .... or f^-1(x) = + ....

why didnt the book do the domain restrictions? i however did see they did restrctions such as x is an element of [0,infinity) for example, however this was only at the end , provided the original, f(x) was a one to one. The chapter i just had answers such as those attached.