• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Discover how to solve inverse functions both graphically and algebraically, whilst investigating their relations, properties and patterns.

Extracts from this document...


Year 11 IB Maths HL – Inverse FunctionsMathematical Investigation

Graphical Determination of the Inverse                                                                         Fergal Banks

Problem Statement: Whilst completing this investigation, I plan to find out three main aspects about inverse functions,

  • Can we find the inverse of any given function graphically?
  • What are the properties of the inverses of some common functions?
  • Do all Functions have an inverse?

Whilst using the method, the function f(x) has an inverse f¯¹ (x) if f (f¯¹ (x))  =  x.

Method: Discover how to solve

...read more.


(3x - 1)/(x + 2) is reflected and becomes, (2x + 1)/(3 – x). This results in a mirror image of the original function.

c)        image02.png

f(x) = x³ is reflected resulting in the inverse function, g(x) = ³√x.



Using the linear function, f(x) = 4x + 8, it is clear that my results in Q2 are indeed correct, as they are confirmed by the inverse function of the above linear function. It is flipped resulting in g(x) =. I worked out the inverse function by working

...read more.


Algebraically, this can proven by showing that the inverse of y = x², is y = √x. This is due to the fact that the inverse function is in fact a mirror image of the f(x). However, as each y value has more than one x value, it cannot be a function.

Conclusion: By completing this investigation, I have been able to find out that all linear and rational functions have an inverse. However, the same cannot be said about quadratic functions because it does not fulfil the criterion of a inverse function, that each y value cannot have more than one x value. All functions that complete the vertical line test will have an inverse function.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Logarithms. In this investigation, the use of the properties of ...

    So due to the information provided by the four sequences, we can come to the conclusion that the formula of logmnmk can be replaced with the expression k/n where k is a constant. Below is a graph showing the values of the three sequences Part 2 Given the following sequences,

  2. Investigating Quadratic functions

    Also, if the coefficient is positive, the opening will be facing upward, and if it's negative, the opening will be facing downward.

  1. Math Investigation - Properties of Quartics

    Equation of a line which passes from any two points can be found by the formula. We will now substitute the known values (co-ordinate points) and find out the equation of line. Y1 = 15 Y2 = 23 X1 = 3 X2 = 1 Therefore, the equation is: Y =

  2. Investigating the Graphs of Sine Functions.

    and my conjecture of it, I can conclude that they are equal and therefore my conjecture for its transformations and its characteristics was right. Graph of y= sin3(x+1) Conjecture: y= sin3(x+1) is equal to y= sin(3x+3) and is therefore y= sin3(x+1)

  1. Population trends. The aim of this investigation is to find out more about different ...

    This is the model I am going to develop as it closely associates itself to the data, not when is multiplied by one but by less than one. This curve is and there are two relevant numbers to what the investigation gives in terms of numbers, the in the equation

  2. LACSAP's Functions

    Afterwards, I decided to plot the row numbers of LACSAP's fractions with the numerators and the newfound equation nC2, or n!/2!(n-2)! Task 2 - Plot relation between the row number and Numerator, write general statement about it n Numerator 1 1 2 3 3 6 4 10 5 15 This is a graph of Numerator (y - axis)

  1. In this investigation, I will be modeling the revenue (income) that a firm can ...

    for quarter 1 is correct. Moving onto the 2nd, 3rd and 4th quarters, we can apply the same method of finding the gradient, then substituting the values with P and Q in order to get the linear demand equation. Calculations to get Linear Demand Equations for 2nd, 3rd and 4th quarters: Quarter 2 3 4 Values of P & Q Gradient 1.

  2. The purpose of this investigation is to explore the various properties and concepts of ...

    Application of a mathematical model, with partial effectiveness. Partly accurate and generally incomplete solutions to mathematical problems set in applied or theoretical contexts. Attempted interpretation of the mathematical results in the context of the problem. Some awareness of the reasonableness and possible limitations of the interpreted results. Attempted development or testing of a reasonable conjecture.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work