VCE Methods Question Thread!

[nina_rox]

Another question:

What is the domain and range of the composite function f(g(x)) if the shape of the composite was unknown? Is the domain the domain of the inner function? What about the range?

Thanks!!

[availn]

Another question:

What is the domain and range of the composite function f(g(x)) if the shape of the composite was unknown? Is the domain the domain of the inner function? What about the range?

Thanks!!

If f(g(x)) exists, then yes, its domain is the domain of g(x). As for the range, that is something that you just have to figure out. It is best to sketch it, as you need to have some sort of idea what it looks like.

[link125]

Just wondering how I could rearrange this:



to this

[b^3]

Rationalise the denominator.

[link125]

thanks!

[soccerboi]

I asked this a few days ago but just to put it into my own words: When they ask for when a function is strictly increasing or decreasing, we include the initial point/endpoints or any points of inflections.

Can someone clarify?
Thanks

[e^1]

I asked this a few days ago but just to put it into my own words: When they ask for when a function is strictly increasing or decreasing, we include the initial point/endpoints or any points of inflections.

Can someone clarify?
Thanks

From VCAA:

Source: http://www.vcaa.vic.edu.au/Documents/bulletin/2011AprilSup2.pdf


This definition does not require f to be differentiable, or to have a non-zero
derivative, for all elements of the domain.

So yes, you include endpoints or such stationary points when being asked to specify a domain, where the function is strictly increasing or decreasing.
Refer to the VCAA supplement for examples.

[nina_rox]

Another question:

What is the domain and range of the composite function f(g(x)) if the shape of the composite was unknown? Is the domain the domain of the inner function? What about the range?

Thanks!!

If f(g(x)) exists, then yes, its domain is the domain of g(x). As for the range, that is something that you just have to figure out. It is best to sketch it, as you need to have some sort of idea what it looks like.

Thank you!

[nina_rox]

Also sorry to be annoying:

How do you find the general solution of:

cos(x) + cos(3x) = 1/2

I found this equation in the study design. Thanks!

[Jenny_2108]

Also sorry to be annoying:

How do you find the general solution of:

cos(x) + cos(3x) = 1/2

I found this equation in the study design. Thanks!

cos(x) + cos(2x+x)=1/2
expand them all, then use double angle formula then solve for cos(x)

[dfgjgddjidfg]

vcaa 2011 2.e help???
how can i use a tree diagram for this

[Thisusernamealreadyexistsalreadyexists]

Also sorry to be annoying:

How do you find the general solution of:

cos(x) + cos(3x) = 1/2

I found this equation in the study design. Thanks!

cos(x) + cos(2x+x)=1/2
expand them all, then use double angle formula then solve for cos(x)

Hold on, are we supposed to know double angle formulae?

[aishuwa1995]

Also sorry to be annoying:

How do you find the general solution of:

cos(x) + cos(3x) = 1/2

I found this equation in the study design. Thanks!

cos(x) + cos(2x+x)=1/2
expand them all, then use double angle formula then solve for cos(x)

Hold on, are we supposed to know double angle formulae?

My teacher told us to put it in our bound references and she said it would be very very very unlikely to come up in exam 1

[charmanderp]

If it comes up in either exam I propose we all revolt against VCAA.

[Tonychet2]

what is the logic behind VCAA 2011 exam 1 question 4b?

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2011mmcas1-w.pdf

is this right? ::

step 1: A square root functions contents must be positive
step 2: therefore (X+8) (X+2) must be both positive? so x<-8 ad x>-2? is that all?