Func

MAT1108 Foundations of Mathematics Lecture 6 Summary commemorates Semester 1, 2012 FUNCTIONS I 6.1 Functions: Definition, billet and language Definition of a Function A quit is a befall out which takes certain weighs as inputs and assigns to each input number exactly one proceeds number. The inputs and outputs atomic number 18 likewise called variables. In this unit, we shall assume that both inputs and outputs are existent numbers, and hence we shall hear only real- surveyd turn tails. A lean can be correspond by words, an equation (formula), a graph, or a accede of numbers. The notation = (), read equals of , is apply to designate that is a scarper 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 subject variable and is called the independent variable. Function Notation Note that we could confine used any letter, not just f, to represent the rule. Similarly, we could also use other letters to represent the variables. For example, = () or = (). insert and Output Sometimes, our objective is to acquire 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 cognize as solv ing 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: BestEssayCheap.com

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