Bob

]]>Bob,Did you become the administrator? Congratulations, bob for your promotion!.

WHAT IS THIS???

]]>Think of a function as being a box into which you can input a number and another number is output. f and g are two such functions.

If you join the output from g to the input for f we get a composite function. To find out what single function is the same as the composite function you have to apply first g (which means you have an expression in x and put that through the second box for f.

g(x) = 3x + c so the box takes a number, times it by 3 and then adds c. If that is the input for the f box the output from f looks like this:

2(3x + c) + 7 The input is (3x + c) and this is times by 2 and 7 added.

So the composite function for (f o g) is 2(3x + c) + 7. You can simplify this yourself.

You might think at first that g o f will give the same result but it doesn't. First do f ... 2x + 7 and then make this the input into g ... 3(2x + 7) + c

We want these to be equal so just make an equation by putting them equal to each other. The x terms cancel out (why?) so you're left with an equation for c.

There is a MIF page on this here: http://www.mathsisfun.com/sets/function … ition.html

Note The x comes after the function letter [eg. f(x) not (x) f ] so when you want to apply a second function you have to put it before the first. eg g(f(x)) means apply f then g to the result. This can be confusing but think about log(sin(x)) for example. o is used to indicate that we are combining functions.

Hope that helps,

Bob

]]>If 1 & -1 are the zeroes of the polynomial p(x)=Lx^4+Mx^3+Nx^2+Rx+P=0, prove that L+M+P=M+R=0. [JEE mains 2014, AIEEE 2006, IIT 1998]

I think it should be

If 1 & -1 are the zeroes of the polynomial

Although it is headed 'Percentage Change', the first part of it covers your problem completely, by giving:

1. the definition of *percentage increase*;

2. two different methods of calculating *percentage increase*;

3. one calculation example for each of the two methods.

MathsIsFun's treatment of this topic is excellent and very clear.

]]>how to find order of an recurrence relation

for example :

an= an-1 + an^2-2

there order of this function is "2"

how is that be?

and what is the meaning of order

please help me,

]]>Thank you!

]]>we have:

you could also have:

These are incorrect. All of the forms involving the natural logarithm for the answer must have absolute value

bars where the logarithm of the quantity is being taken of in these examples, not just parentheses.

This goes for the rest of your posts in this thread.

]]>Instead of printing them in 'output format' within Mathematica (which takes forever), this code prints them in text format to a file that I called "list.txt", which M automatically places into my Windows 10 'Documents' folder.

The file contents then print into M's output pane...in a blink!

The contents of the file are automatically overwritten each time the program is run, but renaming the file in the code before an evaluation will create a separate file. That only needs to be done in one location...the 'f' variable in the first line.

The results are listed in descending numerical order within each group of deducted primes - as per the OP's method - and those deducted prime groups appear in ascending order of deducted primes (see example in the hide box in the previous post).

I've included a counter that returns the total number of odd-prime trios.

The next code displays the results in ascending order:

These codes also work in the online Wolfram Programming Lab (although the output is limited to 150 lines), but not in the Mathics link that worked on my earlier code versions.

]]>