Units 1 Questions thread

[cltf]

I am in dire need of help, simply the matter is I seem to have lost my ability to answer simple questions:

1. For find the largest domain so that the INVERSE function does exist, then state the inverse function.
My answers: and

2. a can has a volume of the height is "h" the radius is "r"
express "h" in terms of "r"
Then, Show that the total surface area, of the can can be given by

3. An open tank is made from a sheet of metal 84cm by 40cm, by cutting squares of X length of the corners, express the volume of the tank in terms of X, hence state the maximal do mail of your function for V, the volume of the tank.

4. Make "a" the subject in

[the.watchman]

Here you go! (if you need more explanation, I'll tell you at school tomorrow)

(1) For this the 'largest' domain is actually , because it is slightly 'bigger' than what you had (sounds weird I know but the extra four units makes a big difference)

So for : Let







BUT if the domain of f is [-2,infinity), then the range of f^-1 is also [-2,infinity)

So is rejected





(2)



So



(i think you put a minus in accidentally?)



(3) Visualising the sheet (as a net for the tank),

Length is (84-2X)cm and width is (40-2X)cm and height is Xcm

so , 0<X<20 (because if , then the width is zero, or negative)



(4) x abc:

[cltf]

Ahhh that new domain would explain so much! It explains my Y intercepts when I tried to sketch it, I should have known.

ah cool, i was pretty close to most of them, that's good to know. thanks once again!

one more think, just in reference to question what is the maximal domain? How do I find it?

[TrueTears]

x(84-2x)(40-2x)=v

the domain is R. I am assuming you are not relating this question to any specifics. If so then you must apply restrictions, i haven't read any of the above posts.

ALL polynomial functions have domain of R (try prove this very fun proof! think about the converse, what if they didn't have a domain of R?)

[the.watchman]

Sorry, but for the question scenario, it is 0<X<20

For the tank to exist, the height, length and width all must be greater than zero

So, for height: X>0
For length: 84-2X>0, X<42
For width: 40-2X>0, X<20

For all these to be true, the maximal domain must be 0<X<20

[cltf]

if and how do i find the intersection point?

also what is I meant to do here?
The value(s) of "m" that will give the equation two real roots lie in the following
a)
b)
c)
d)
e)

[moekamo]

1 let f(x) = x and solve for x, this is the x and y value of the intersection point/s


2.

for 2 real roots the discriminant must be greater than 0:


so



by doing it graphically we can see that

[cltf]

1 let f(x) = x and solve for x, this is the x and y value of the intersection point/s


2.
so

so when




we can just factorize and ignore the 12?

and i dont get the intersection point part.

[the.watchman]

(1)
As you should know, the graph of the inverse is a reflection in the line y=x
So the graphs of the inverse and the original function should intersect on the line y=x

Therefore, instead of solving , it will suffice to just solve
Also, the y-values are the same as the x-values (because y=x), which is what moekamo said

(2)
It's not 'ignoring' the 12, it's dividing both sides by 12

[m@tty]

The 'largest' domain is actually , because it is slightly 'bigger' than what you had (sounds weird I know but the extra four units makes a big difference)

If asked for the maximal domain would the other domain(which is equally infinite) be marked wrong?

[the.watchman]

The 'largest' domain is actually , because it is slightly 'bigger' than what you had (sounds weird I know but the extra four units makes a big difference)

If asked for the maximal domain would the other domain(which is equally infinite) be marked wrong?

I'm not sure, but seems 'more right', eh?
I have no idea though...

[cltf]

The 'largest' domain is actually , because it is slightly 'bigger' than what you had (sounds weird I know but the extra four units makes a big difference)

If asked for the maximal domain would the other domain(which is equally infinite) be marked wrong?

I'm not sure, but seems 'more right', eh?
I have no idea though...

If you sketch it is more correct.

[the.watchman]

The 'largest' domain is actually , because it is slightly 'bigger' than what you had (sounds weird I know but the extra four units makes a big difference)

If asked for the maximal domain would the other domain(which is equally infinite) be marked wrong?

I'm not sure, but seems 'more right', eh?
I have no idea though...

If you sketch it is more correct.

That's what I thought, but I'm not sure if the other one would be marked wrong.
Clarification anyone?

[m@tty]

The 'largest' domain is actually , because it is slightly 'bigger' than what you had (sounds weird I know but the extra four units makes a big difference)

If asked for the maximal domain would the other domain(which is equally infinite) be marked wrong?

I'm not sure, but seems 'more right', eh?
I have no idea though...

If you sketch it is more correct.

It *appears* more correct.

But against the enormity of infinity 4 units is infinitesimal, even to the point of becoming irrelevant.

Technically they're equal, but logically they are different. I suppose they should be considered of different sizes, though I have never seen this addressed...

[cltf]

got a dilemma.
In the methods unit 1 semester exam, no doubt there will be a cubic graph, how do i find the maximum and minimums?
Because my cas either keeps giving me a not accurate enough pinpoint, or not enough decimal places. Is there any other method CAS aside i can use to find the max and min? cause my friend mentioned something about differentiation...