Math Is Fun Forum

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Functions Problems

Hello, I do not know the answers to these problems.

1)

2)

3)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Functions Problems

hi denis_gylaev

Q1)  f o g means apply g and then f to the result:

f o g (x) = 2.(3x + c) + 7

Do a similar thing for g o f and set them equal.

Q2)  This will get the equation of the line AB:

By substituting the known values of x and y you can get equations to find a and b.

Q3)  Just set f and g  equal and solve for x.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Re: Functions Problems

Hi Bob, thank you so much for the help.

For Q2, I got (-1,-2) and (1,2) and for Q3 I got (-1, 3)

However, I still do not understand what you mean for number 1. Please advise.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Functions Problems

hi denis_gylaev

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob