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

]]>Inherent love for numbers!

]]>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

There is a goddess in Greek mythology called **Eunomia**, as well as an asteroid named after her.

]]>You are welcome to ask and tell about your findings.