1 / 9

6.7 Inverse functions

6.7 Inverse functions. What is an inverse function?. Inverse Relation: If an relation pairs of element of a of its domain and b of its range pairs b with a. For example: if (a, b) is an ordered pair of a relation then (b, a) is an ordered pair of its inverse

temple
Télécharger la présentation

6.7 Inverse functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 6.7 Inverse functions

  2. What is an inverse function? • Inverse Relation: If an relation pairs of element of a of its domain and b of its range pairs b with a. For example: if (a, b) is an ordered pair of a relation then (b, a) is an ordered pair of its inverse • Inverse function: if both a relation and its inverse are functions

  3. Find an inverse given a table or graph • What is the inverse of the given relation? • Switch your x & y 1) plot the pts. and rewrite 2) switch to (y,x) 3) plot (y, x)

  4. Finding the inverse of a function • Change f(x) to y • Switch your x and y • Solve for y • Rewrite as f-1(x) • Determine if f-1(x) is a function

  5. examples Find the inverse function and determine if it’s a function (We will be using the index cards to the first 2 examples) • 1. f(x) = 3x + 5 • 2. f(x) = 6x – 8 • 3. f(x) = x2 + 4 • 4. f(x) = 5 – 2x2 • 5. f(x) = 4 – 3x

  6. Determine domain of inverse function • Domain: all your x values For any liner, quadratic, cubic, etc (where the exponent is a whole #) your domain is always: all real numbers or (-∞, ∞) If there is an even root (sq. root, 4th root etc.), you need to determine what value of x will make the expression = 0, that x value is the minimum domain value & will be written as [#, ∞) Examples: use the 5 example we just did

  7. Determine the range • Range is all the y values • Determine if your function has a minimum or a maximum value (not both) • If there is not just 1 minimum or maximum your range is: all real numbers or (-∞,∞) • If there is just 1 minimum then your range is: [minimum y value, ∞) • If there is just 1 maximum then your range is: (-∞, maximum y value] - examples: let’s look at the 5 we did

  8. Graphing • 2 ways: You must graph both the relation & its inverse • 1st way: by hand • A) make a table of values (w/ a minimum of 5 points – if linear pick 2 “-”, 0, and 2 “+”, if it’s quadratic find the vertex & then pick 2 < the vertex and 2 > the vertex) • B) plot each point and connect 2nd way: calculator • A) enter both graphs on the calculator • B) sketch what you see, make sure you have accurate points, so you may have to look at the table of values

  9. Composition of Inverse Functions • If f and f-1 are inverse: (f-1˚ f)(x) = x and (f ˚ f-1)(x) = x for x in the domains of f and f-1 respectively Examples: determine if the functions are inverses • f(x) = 10x – 10 and f-1(x) = x +10 10 2. f(x) = 3 – 7x and f-1(x) = x – 7 3

More Related