function

Video I

Function
Function is special relation that set each member of domain with exact one from member of kodomain.
Let the fuction f is defined by f(x)=x+1
If 2f(p)=20. What is the value of f(3p) ?
f (x)=x+1
2f(p)=20
f(p)=10
f(p)=p+1=10
p=10-1=9
What is f when x=3p ?
x=3.9=27
So value of f(3p)=f(27)
f(27)=27+1=28
If the function h is defined by h(x)=g(2x)+2, h(1)=2, h(2)=-2.
What is the function g and function h ?
h(1)=g(2)+2=2
g(2)=2-2=0
h(2)=g(0)+2=-2
g(4)=-2-2=-4
Let the function g(x)=ax+b
g(2x)=g(2)=2ax+b=0
g(2)=4a+b=0
g(2x)=g(4)=2ax+b=-4
g(4)=8a+b=-4, so b=-8a-4
b=-8a-b-4 substitute to 4a+b=0
4a-8a-4=0
-4a=4
a=-1
Because of 4a+b=0, so
-4+b=0
b=4
g(x)=ax+b=-x+4
h(x)=g(2x)+2=-2x+4+2=-2x+6
So the function g is g(x)=-x+4, the function h is h(x)=-2x+h

Video II

Factor of polynomial
Factor of polynomial is a divider of polynomial without remainder.
Let
3rd power of x minus 7x minus 6 in bracket divided by x minus 3 in bracket equal x squer plus 3x plus 2, without remainder.


From this example, we know that x-3 is a factor of those polynomial.
Because of

0=(x-3)(x+1)(x+2)
x-3=0, so x=3
x+1=0, so x=-1
x+2=0, so x=-2
x=3; x=-1; x=-2 is called roots of polynomial

Video III

Pre Calculus
Let f(x)=(x+2)/(x-1), when x=1, value of function f is not defined. So, not all value is a rational function.
In conclusion function f is not continue.
If y equal x square minus x minus 6 in bracket devided by x minus 3 in bracket , when x=3, value of y is not defined. But if
y=[(x-3)(x+2)]/(x-3)=(x+2), when x=3, value of y is defined.
So, this function is continue.

Video IV

Invers function
f(x,y)=0
Function y=f(x) : VLT
x=g(y) : HLT
If y=2x-1 and y=x
y=x substitute to y=2x-1
x=2x-1
-x=-1
x=1
y=x=1
So intersection of line y=2x-1 and y=x is (1,1)
Invers function in a return value from function f(x)
Let y=2x+1
y-1=2x
1/2y-1/2=x
So invers function from y=2x+1 is y=1/2x-1/2

To Express Mathematics

Intan Widya Kusuma
07305141039
Mat. R'07

To Express Mathematics

Meaning :

Kecenderungan : inclining
Terjalin : connected
Redefine : mendefinisikan kembali / menegaskan
Prefecture : provinsi

sentence
• A quarter value in each series has inclining approximate 1 not meaning that this series is convergen.
• A function is called continue if only their graph is a line which always connected.
• Monotonous series can redefine a series which not visit descend or not ascend.
• Java consist of 5 prefecture.