Functions by mstfdemirdag
Upcoming SlideShare
Loading in...5
×
 

Functions by mstfdemirdag

on

  • 411 views

mstfdemirdag.com

mstfdemirdag.com

Statistics

Views

Total Views
411
Views on SlideShare
411
Embed Views
0

Actions

Likes
0
Downloads
8
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Functions by mstfdemirdag Functions by mstfdemirdag Presentation Transcript

    • FUNCTIONS
    • The Domain of a Function Example: The domain is the set of all real numbers for which the expression is defined as a real number. f(x) = 2x + 3 D=R g(x) = 2x + 3 D=R Example: f(x) = g(x) Example: 1 f (x ) = x −4 D = R – {4} f (x ) = x D = R+ g(x) = x f (x ) = 5 f (x ) = 2 − x 2x − 6 x f (x ) = 2 f (x ) = x 2 − 4 x −9 f (x ) = Equal Functions Two functions are equal if and only if their expressions and domains are equal. 2 x x D=R f(x) ≠ g(x) D = R – {0} Even and Odd Function A function is called even if f(-x) = f(x) A function is called odd if f(-x) = -f(x) Example: State whether each of the following functions are even or odd function. f(x) = 3x2 + 4 h(x) = 2x3 g(x) = x m(x) = x3 – 1
    • What is use of even and odd functions? Graph of a function is symmetric respect to y-axis if it is even. Graph of a function is symmetric respect to origin if it is odd. Example: Classify whether the following functions are even or odd.
    • Vertical Line Test: A graph is a function if every vertical line intersects the graph at most one point. Example: Find f + g, f - g, f·g, and f/g Operations on Functions: Homework: Page 53 check yourself 13 Homework: Page 53 check yourself 13
    • Composition of Functions Now let’s consider a very important way of combining two functions to get a new function. Given two functions f and g, the composite function f o g (also called the composition of f and g) is defined by (f o g)(x) = f( g(x) )
    • Example:
    • Inverse Functions Horizontal Line Test One-to-One Function A function f is one-to-one if and only if A function f with domain D and range R is a every horizontal line intersects the graph of f in at most one point. one-to-one function if either of the following equivalent conditions is satisfied: (1) Whenever a≠b in D, then f(a) ≠ f(b) in R. (2) Whenever f(a) = f(b) in R, then a=b in D. Example: Example: Check whether the following functions are one-to-one. f(x) = 3x + 1 g(x) = x2 - 3 h(x) = 1 - x
    • Inverse Function Let f be a one-to-one function with domain D and range R. A function g with domain R and range D is the inverse function of f, provided the following condition is true for every x in D and every y in R: y = f(x) The two graphs are reflections of each other through the line y = x , or are symmetric with respect to this line. if and only if x = g(y) How to find inverse of a function Solve the equation x = f(y) for y. f(x) = 3x + 7