Math Is Fun Forum

matikastat

Member

Registered: 2006-09-14

Posts: 5

Functions PLEASE HELP

If someone would be so kind to solve these problems and explain the hows and the whys:

(x<2> means x²)

1.  g(x)=1-3ln(1-2x)

a)inverse function?
b)draw it

2. f(x)=- x / x<2>-3y +2

a)domain of the function?
b)extremes of the function?

3. with gauss-jordan procedure solve this equation system

x-2y+3z=4
2x+z-z=5
3x-z+2z=5
5x+z=6

4.

5. calculate the surface between the curves: 2e<x>+y=0  y<2>-4=0  y=0

6. the matrix is A= 0 -2 3
                            0 0 4
                            0 0 0
calculate (I-2A)<1>

7. f(x)=2+e<1-x> and g(x) = (2-x)/3. Define these functions(domain, picture and rule):
a)f ºg
b)(g º f) <-1>

8.Test the extremes of the function f(x)=(2x<2>+x+2)/x<2>+1

9.Using integrals calculate the surface between the curves:
y-x<2>+1=0
x-y=0

You can send me step by step solutions to these tasks to matikastat@yahoo.com

Last edited by matikastat (2006-09-14 02:01:00)

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: Functions PLEASE HELP

Thought I'd reply to the thread, rather than e-mailing you, so anybody else who's wondering what the solutions are can see. Anyway, there's quite a lot there, so one at a time, me thinks!

Now, as for part (b), it sure does look like a "rather ugly" function to draw... but if you're only doing a sketch, it's not so bad. The basic form is that of

. Additionally, the constant in front of it will "shift" this function up, so instead of steadilly approaching zero, it will approach 1/2. Also, the graph of this function will cut the g[sup]-1[/sup](y) axis when y = 0, at

, and since

, you know that this intersection will take place below the y-axis. So a sketch of the graph will look like this:

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Bad speling makes me [sic]

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: Functions PLEASE HELP

2. f(x)=- x / x<2>-3y +2

Two things I was wondering - firstly, do you mean

or

? Secondly, is that y supposed to be an x, or is it a constant?

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Bad speling makes me [sic]

matikastat

Member

Registered: 2006-09-14

Posts: 5

Re: Functions PLEASE HELP

Thank you so much!
If you find the time for other tasks I would really appreciate it, I have until monday.

I meant the first case, and as for the other question the task was given in that form so I'm not sure what do you mean.

Last edited by matikastat (2006-09-14 03:33:22)

matikastat

Member

Registered: 2006-09-14

Posts: 5

Re: Functions PLEASE HELP

If you find it that some tasks are impossible or smth. it doesn't matter. you can just pick other nearly indentical task because the point is to see step by step solutions  of each type of tasks, not the specific task itself.

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: Functions PLEASE HELP

I'll do question 2 quickly, but I have to say I'm a little confused. Whoever has set the question has written f(x), which implies a function that is dependant upon only the value of x, but has put a y in the expression - are you likeley to be asked about the maxima/minima of expressions of more than one variable? I'll assume it is a typo and should read

. In this case, the domain of the function (I assume you know what domain and range are? If not, there are plenty of places on the webby that'll explain it) is any value of x where the denominator is non-zero.

So, we need to look for the values of x such that

.

can be factorised to

, so

where x = 1 or x = 2. The domain of the function is therefore the set of real numbers with 1 and 2 removed, or

As for the second part, we need the maxima and minima. Differentiate the function (am about to finish work so I don't have time to type it all out yet) and find where the derivative is zero. You should find extreme points at

and

.

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Bad speling makes me [sic]

matikastat

Member

Registered: 2006-09-14

Posts: 5

Re: Functions PLEASE HELP

OK, just  take your time to type all of the procedure-every little step to each solution.
Thanks.

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: Functions PLEASE HELP

OK, just  take your time to type all of the procedure-every little step to each solution.
Thanks.

To be fair, if they're asking you to do it, you should be able to differentiate it. Write the function as

and use the product rule.

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Bad speling makes me [sic]

Dross

Member

Registered: 2006-08-24

Posts: 325

Re: Functions PLEASE HELP

5. calculate the surface between the curves: 2e<x>+y=0  y<2>-4=0  y=0

Can I ask who set these questions? Are you sure you've copied them into your post correctly? Either I'm going mad or there are a lot of typos. This question asks for the area (presumably) of the area bounded by the curves

,

,

and

. Draw these on a graph - I cannot see that it makes any sense at all!

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Bad speling makes me [sic]

matikastat

Member

Registered: 2006-09-14

Posts: 5

Re: Functions PLEASE HELP

Ok, english is not my native language, so I have to translate some terms literally.
To answer your question-calculate the measuring number of the surface between the curves. This would be more accurate. Does this make more sense, there are no typos, that's why I told you if you find something impossible or strange you should just pick a nearly indentical problem from that particular area.