14/1/13 Lesson Summary

By Carissa
Inverse Functions

• To express inverse function: ƒ⁻¹
• ƒ⁻¹(x) is not equal to 1/f(x)
• An inverse function is a reflection of the original function (can be seen clearly on a graph

To find an inverse, introduce y 

Example:

f(x) = 2x+3

2x+3 = y

x = y-3/2 (make x the subject)

ƒ⁻¹(x) = x-3/2

1. What is the Inverse of an Inverse function? Illustrate your answer with an example.

It will be the the originally function.

The inverse of f(x) = 2x+3 is  f(x) = x-3/2. The inverse of f(x) = x-3/2 (the current inverse) is f(x) = 2x+3, which is the original inverse.

2. Do all Functions have an inverse? Substantiate your statement.

Not all functions have an inverse. 

Sin^-1 does not have a inverse function as it is not possible to reflect in on a graph as shown.

http://hotmath.com/hotmath_help/topics/inverse-trigonometric-functions.html

However, if we control the domain, it can become a inverse function.

3. How can we illustrate an Inverse Function graphically?

http://everythingmaths.co.za/grade-12/06-functions-and-graphs/06-functions-and-graphs-04.cnxmlplus

Polynomials

• Many-nomails
• Standard form (x^2+x+1) tells you the maximum number of solutions.

Homework for today:

• Read this post. What are the common mistakes students make when dealing with algebraic equations.
• - Complete the questions on the Maths blog
  - Worksheet A01A - Functions (By Tuesday)
  - Worksheet A01B - Polynomials (By Thursday)
  - Worksheet A01C - Long Division (By Friday)