stretch yourself – what is the domain and range of
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Stretch Yourself – What is the domain and range of..
)4( xxy
)5(
1
xxy
)2(
1
xxy
How Many “functions”?
2)1(
1
2sin xe
2)1(
1
2sin xeComposite Functions
)(xk
)(xj
)(xi)(xh
)(xg
)(xf
x12xx
1xexsin2x
Aims: To be able to perform a composition of functions and to be able to find a single function
that performs a composition of functions at once.
Lesson Outcomes Name: Know what is meant by a
composite function. Describe: How composite functions
are denoted. The difference between fg(x) and gf(x) in terms of functions f(x) and g(x)
Explain: How you can combine functions into a single function algebraically (and deciding which composition makes a function).
Notations Functions are performed right to left
inside to out. fg(x) means perform g(x) on a value then
put the result in place of x into f(x) gf(x) means perform f(x) on a value then
put the result in place of x into g(x) This process can be written algebraically.
To write fg(x) replace every x in f(x) with the whole of the function g(x) ** don’t forget brackets**
Examples
3)( xxf
2)( xxg Find:
(a) gf(2)
(b) fg(2)
(c) gf(x)
(d) fg(x)
Composite Functions
2)3()( xxf
9
2)(
x
xg
xxh 34)( Write down and simplify 6 composite functions made from these functions
A composite function is a function that is made from combining two or more functions
This concept is one of the most vital elements to help with differentiation and integration this year!!!!!!!
It really helped with my UCAS
application
xxa )( )sin()( xxb
xexc )(x
xd1
)(
2)( xxe 3)( xxf
)ln()( xxg
Composite Functions
Click to start the 10 minute timer
Something on Domains and Ranges
fab(x)
What happens when you find fab(3π/2)? (radians)xxa )(
)sin()( xxb
3)( xxf
5 10 15 20
2
4
6
8
10
12
14
x
y
Devising The Composition Being Told a Composition and
finding the order can be challenging try these
fg(x)
gh(x)
fhg(x)
hf(x)
gg(x)
hfg(x)
Round-Up What is a composition of functions?
What is the difference between fg(x) and gf(x)?
I can describe a composite function as a single function in algebra. (Hands-Up)
I can combine functions in different orders to achieve different transformations. (Hands-Up)
You have one minute to memorise as much as you can from these picturesTIME’S UP!
What colour was the television?
How many holes were in the cheese?
Which way were the toes of the shoes pointing?
Talk to the person next to you about strategies YOU use to memorise facts and formulas
3.141592653589793238462643383279There are many facts and formulae in Maths that will make problem solving seem much easier. You CAN do it if you make the effort!
Increase your Learning Power!
How well do you know the number pi?