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

Year 11 IB Maths HL – Inverse Functions Mathematical 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 inverse functions both graphically and algebraically, whilst investigating their relations, properties and patterns.

2.

a)

The linear function, f(x) = 2x + 4 is reflected. So the points on the graph, (0,4) become (4,0).

b)

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

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