Inverse Functions (Cambridge (CIE) A Level Maths) : Revision Note
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Inverse Functions
Inverse functions
An inverse function is the opposite to the original function
It is denoted by f-1(x)
An inverse only exists for one-to-one functions

Graphs of inverse functions
The graphs of a function and its inverse are reflections in the line y = x

Domain and range of inverse functions

The range of a function will be the domain of its inverse function
The domain of a function will be the range of its inverse function
How do I work out an inverse function?
Set y = f(x) and make x the subject
Then rewrite in function notation
Domain is needed to fully define a function
The range of f is the domain of f-1 (and vice versa)

... and finally …
A function (f) followed by its inverse (f-1) will return the input (x)
ff-1(x) = f-1f(x) = x (for all values of x)

Worked Example

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