Monday, 14 January 2013

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

3. How can we illustrate an Inverse Function graphically?

  • 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) 

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