Download presentation

Presentation is loading. Please wait.

1
Inverse Functions

2
Function If for every x there exists at most one y One – to – One Function If for every x there exists at most one y AND for every y there exists at most one x Function Function One – to – One NOT One – to – One

3
**Only one – to – one functions have inverses**

GRAPHICALLY One – to – One Function Inverse

4
**Function and Inverse have Symmetry about the line y = x**

One – to – One Function Inverse Function and Inverse have Symmetry about the line y = x

5
**Find the inverse graph of the function below, if it exists.**

Since not ONE – TO – ONE, no inverse function exists

6
**Find the inverse graph of the function below, if it exists.**

(4.5, 7) (7, 4.5) (0, 3) (-4, 1) (3, 0) (1, -4) (-7, -5) (-5, -7)

7
**Find the inverse graph of the function below, if it exists.**

8
**Finding inverse functions algebraically**

9
**Finding inverse functions algebraically**

PCH ONLY – LOOK AT PROBLEM 68

10
**Derivatives of Inverse Functions**

If f is differentiable at every point on an interval, and f ’ is never zero on the interval, then: is differentiable at every point on the interior of the Interval and its value at the point f(x) is:

11
**Find the derivative of the inverse of f(x) = 5 – 4x evaluated**

at c = ½

12
**Find the derivative of the inverse of evaluated**

at c = 4 Not One-to-One However….One-to-One on [2, 6] which not only includes c = 4, but it also eliminates f ‘ (x) = 0 issue as well Alternative…….

13
**Find the derivative of the inverse of evaluated**

at c = 4

14
**Find the derivative of the inverse of at c = 1**

Similar presentations

OK

3.1 Derivative of a Function Objectives Students will be able to: 1)Calculate slopes and derivatives using the definition of the derivative 2)Graph f’

3.1 Derivative of a Function Objectives Students will be able to: 1)Calculate slopes and derivatives using the definition of the derivative 2)Graph f’

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on marie curie's daughter Ppt on operating system architecture Ppt on kingdom monera facts Free ppt on history of cricket Ppt on satellite orbit magazine Ppt on 10 sikh gurus name Ppt on db2 mainframes definition Ppt on producers consumers and decomposers Ppt on solid dielectrics in series Ppt on waxes chemical structure