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GCSE maths self-inverse functions

Discussion in 'Mathematics' started by gainly, Apr 29, 2019.

  1. gainly

    gainly Senior commenter

    The following question is in Edexcel GCSE Mock Paper 2 Autumn 2018. It seems to assume they should know that if ff(x) = x the function is self-inverse. Of course they could work out the inverse function, but as the question says "write down" and is only one mark this is clearly not what was intended.

    There is no mention of self-inverse functions in the specification. Are they meant to know this? It seems a bit unreasonable to me.

    20. f(x) = (1-x)/(1+x)

    (a) Show that ff(x) = x (3)

    (b) Hence, write down f ^–1(x) (1)

    (Total for Question 20 is 4 marks)
     
  2. gainly

    gainly Senior commenter

  3. BG54

    BG54 New commenter

    Although self-inverse functions are not explicitly mentioned in the specification the two Higher tier textbooks that I have both have exercise questions that would involve the topic, so possibly it's expected that it would be discussed in a lesson?

    e.g My AQA book has the following question :-

    Find the inverse of these functions.

    a. f(x) = 1/x
    b. g(x) = 2 - x

    Comment on your answers
     
  4. gainly

    gainly Senior commenter

    Thanks; two of my tutees (from different schools) had been given the paper and certainly neither of them knew about this, although they did know how to find the inverse function.
     
  5. BG54

    BG54 New commenter

    Yes, on reflection I'm inclined to agree with you that the question is a little unreasonable.

    Self-inverse functions are specifically mentioned and defined in Edexcel's Year 2 A-level text on p38 despite not being explicitly mentioned in the A-level specification. This seems a little at odds with the expectation of the mock GCSE question and the absence of any specific use of the term "self-inverse function" in the GCSE texts.
     
  6. gainly

    gainly Senior commenter

    I got them to work out the inverse function by re-arranging. When they realised it was the same as the original, I explained about self-inverse but told them I didn't really think they needed to know this.
     
    BG54 likes this.

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