Download f (x) f (x) g(x) fg(x) gf (x)

Functions
The domain is what x can be
The range is what y can be
Inverse Functions
f
−1
( x)
To find an inverse function:
1. Switch x and y
2. Rearrange to make y the subject
On a graph it is a reflection in the line y = x
Composite Functions
f (x ) g ( x)
fg ( x) means put g into f
gf (x) means put f into g
The Exponential and Logs
y=e
x
1
y=ln ( x)
1
ln( x) means log e x
ln( x)is the inverse of e
x
Iteration
U n+1 =√U n + 5
U 0=2
U 1=√(2)+5=√ 7
U 2=√( √7)+5=2.765(3dp)
U 3=√ ( ANS )+5=2.787( 3dp)
U 4=√( ANS )+ 5=2.790(3dp)
U 5=√( ANS )+5=2.791( 3dp)
U 6=√( ANS )+5=2.791( 3dp)
f ( x )=0 has a solution between a and b if
f ( a)and f ( b) have different signs
Transforming Graphs
y= f ( x )
(4,3)
x
1
x
(-2,-2)
y= ∣ f ( x) ∣
(4,3)
x
(-2,2)
x
1
y= f (∣ x ∣)
(4,3)
x
(-4,3)
x
1
Trigonometry
1
=cosec(θ)
sin(θ)
1
=sec (θ)
cos(θ)
1
=cot(θ)
tan(θ)
2
2
cos θ +sin θ=1
2
2
1+tan θ=sec θ
2
2
1+cot θ=cosec θ
sin(θ) = sin(180−θ)
cos (θ) = sin(360−θ)
tan (θ) = tan(θ+180)
Trigonometry
In the Formula Book
sin( A± B)=sinAcosB±cosAsinB
cos ( A±B)=cosAcosB∓sinAsinB
tanA±tanB
tan (A±B)=
1∓tanAtanB
Not in the Formula Book (but you can make
them by substituting B for A)
sin(2A)=2sinAcosB
cos (2A)=cos 2 A−sin2 A
2tanA
tan (2A)=
2
1−tan A
To put something in the form
R sin(θ±α) or R cos(θ∓α):
-Compare to compound angle formula
2
2
2
-Find R using pythagoras: R =a + b
-Find alpha by dividing sin by cos to get tan
Differentiation
Chain Rule
dy du dy
= ×
dx dx du
Product Rule
y=uv
dy
du
dv
=v + u
dx
dx
dx
Quotient Rule
u
y=
v
du
dv
v −u
dy
dx
dx
=
2
dx
v
Differentiation
Function
e
x
Derivative
e
x
ln( x)
1
x
sin( x)
cos ( x)
cos ( x)
−sin (x )