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These are the Transum resources related to the statement: "Composite functions. Identity function. Finding the inverse function f^{-1}(x)".

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Here are some exam-style questions on this statement:

- "
*\(f(x) = \frac{2x}{5} + 7\) and \(g(x) = 10x^2 - 15\) for all values of \(x\).*" ... more - "
*(a) A function is represented by the following function machine.*" ... more - "
*If \(f(x)=5-4x\) and \(g(x)=4^{-x}\) then:*" ... more - "
*Here is a function machine that produces two outputs, A and B.*" ... more - "
*The diagram shows the graph of \(y=f(x)\), for \(-3\le x \le 4\).*" ... more - "
*The Big Wheel at Fantasy Fun Fayre rotates clockwise at a constant speed completing 15 rotations every hour. The wheel has a diameter of 90 metres and the bottom of the wheel is 6 metres above the ground.*" ... more - "
*The functions f and g are defined as follows:*" ... more - "
*Let \(f(x)=\frac{3x}{x-q}\), where \(x \neq q\).*" ... more - "
*Part of the graph of \(f(x) = {\log _b}(x + 4)\) for \(x > - 4\) is shown below.*" ... more - "
*The functions \(f\) and \(g\) are defined as:*" ... more - "
*The height above the ground, H metres, of a passenger on a Ferris wheel t minutes after the wheel starts turning, is modelled by the following equation:*" ... more

Click on a topic below for suggested lesson starters, resources and activities from Transum.

Transum,

Saturday, August 17, 2019

"There is an Advanced Lesson Starter called Permutable Functions that is open ended but allows students to consolidate their understanding of composite functions."

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.