INVERSE FUNCTIONS

INVERSE FUNCTIONS

By: Andreast Wahyu Sugiyarta PMNR'08

( 08301244011 )

Consider the function f={(1,2),(2,4),(3,6)}. If the components of each orderer pair are interchanged we obtain {(2,1),(4,2),(6,3)}. This new shet of the ordered pairs is called the inverse functions of f-, and is denoted by the symbol f -1. Note that f -1 is also a functions because to aech element in the domain there correspondent exactly one element in the range. This follow from the fact that to each element in the range of f there correspondens exatly one element in its domains . functions such as f that have this property are called one- to- one functions.

If a function f is defined by an equation in two variable, the invers f -1 if it exist, can be defined by interchanging the variable. Because a functions defined by a first- degree equation, y = ax +b (a ≠ 0) is a one- to- one functions (for each x there exactly one y, and for each there is exactly one x), every such linear function has an inverse.

Example:
Consider the functions f defined by y=2x +3. interchanging the variable in the equation we obtain.

x=2y +3
From which we have
y =1/2 (x – 3)

Thus if f(x) =2x +3, then f -1=1/2 (x – 3)
Not all function have an inverse function. For example, if then by interchanging the varuiable we obtain:

x = y2 – 4
y2 = x + 4
y = ± ( x + 4 ) ½


The relation defined by Equation 2 is not a function, since for each x > - 4 in yhe domain, there ae two element in the range. Hence the functions defined by Equation 1 is not a one- to- one functions.

Referensi:
Siswono. 2005. Matematika Inovatif Konsep dan Aplikasinya 2. Solo: Tiga Serangkai

MY PREPARATIONS IN PARTICIPATING MARSIGIT’S LESSON OF ENGLISH 2

MY PREPARATIONS IN PARTICIPATING MARSIGIT’S LESSON OF ENGLISH 2

BY: ANDREAST WAHYU SUGIYARTA PMNR’08 ( 08301244011 )

My preparations in participating lesson of English II is I must capable of language arragnment English cover at sentensess, part of speech, phrase, clause, sentence logic, sentences coherence and word effectiveness,so I can communicating with my lecture and friend’s it has communicated in English mathematic with good and well.
Beside that I want also matters studies that support in university lecture English good and mold media or electronic as internet and other.
Like that after talking by Mr. Marsidit in converence that first is it “ How to communicate mathematic educationing English”.
That to communicate can action with to hear, to talk/ say, to write, to reach, to translate/ understand. And then in mathematic can be found algebra, arithmetic, geometry, calculus statistic, trigonometry, computer/ICT etc.
Beside in mathematic education can unsure teacher student, methode, recaures, classroom etc. recaures is 2 part is it a facilities and tecehingaid.
That to extend by Mr. Marsigit that teaching learning process as motivation, apperception, competence, indicators, evaluations/ assessment, preparation, lesson plan, student worksheet, discussion, alassied teaching, paradigma, theory and contruc visit.
About that English founding as formal→standard are to part is writing and speaking.
Informal are to part is it a writing and speaking.
Then studying of methode that use Mr. Marsigit using an participation, video. Class, discussions, exercise, assignment, internet, web/ blog, test, seeft effort.
Mr. Marsigit also talk about people that competence have an wile, attitude, knowledge, skill and experience.