Func

MAT1108 Foundations of Mathematics Lecture 6 Summary commemorates

Semester 1, 2012

FUNCTIONS I
6.1 Functions: Definition, Notation and language Definition of a Function
A break is a befall out which takes certain weighs as inputs and assigns to each input number exactly one output number. The inputs and outputs are also called variables. In this unit, we shall assume that both inputs and outputs are real numbers, and hence we shall hear only real-valued turn tails. A function can be correspond by words, an equation (formula), a graph, or a accede of numbers. The notation = (), read equals of , is used to designate that is a function of . Thus, applying the rule to the input value, , gives the output value, (). In other words, () stand fors a value of . Here, is called the dependent variable and is called the independent variable.

Function Notation

Note that we could have used any letter, not just f, to represent the rule. Similarly, we could also use other letters to represent the variables. For example, = () or = ().

Input and Output

Sometimes, our objective is to find the output value of a function given that we have an input value. This is cognize as evaluating a function, which means calculating the value of a functions output from a particular value of the input. At other times, the situation is reversed.



We know the output and we want to find the corresponding input. If the function is given by an equation, the input value are solutions to an equation. The process of finding input values is known as solving equations. EXERCISE 6.1 (a) (0) (b) (1) Suppose () = 1 ? + 2 2 , evaluate and simplify the following expressions:

(c) ()

(d) (2)

[ANSWER: (a) 1, (b) 2, (c) 1 ? + 22 , (d) 1 ? 2 + 82 ] EXERCISE 6.2 (a) (3)

Let () = ( 2 + 1)?(5 + ), evaluate the following expressions:

(b) (?1) (c) ()

[ANSWER: (a) (3) = 1.25, (b) (?1) = 0.5, (c) () = (2 + 1)/(5 + )] EXERCISE 6.3 (a) (2)

Given that () = 2 ? 3 + 5, evaluate...If you want to get a full essay, order it on our website: Ordercustompaper.com



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