6 thoughts on “Modulus Addition – 2

  1. sir similarily, for |3x+5| – |5x+3|, minimum value will be not defined as in – infinity but max will be 16/5,by putting the critical value for |5x+3| i.e. -3/5 in the eqn..is that right sir?

    sir what if we have addition and subtraction in the same function?

    • Jaspreet, your answer is correct. We will look at a couple of more complicated examples in the next two posts, which will hopefully clarify what happens when more than two moduli are involved…

      regards
      J

      • Sir, so basically if we are adding two modulus functions then we will get a minima and when we are subtracting two modulus functions we will get a maxima?

        how to check the same if we are working with three modulus functions having alternate postive, negative signs?

      • Not exactly, Jim. When adding, we will get a minimum. When subtracting, it depends which has the higher slope (coefficient of x) so if it is |3x + 2| – |2x – 5| then the +ve modulus has a greater slope and hence there will be a minimum (just like a normal +ve modulus) but if it is |2x + 3| – |5x + 7| then the negative modulus has a higher slope and hence we will get a maximum.

        For three or more moduli, the cumulative slopes will throw us a hint. For example for |2x + 3| + |6x + 2| – |4x + 5| – |5x – 3| the slopes are 2 +6 – 4 – 5 which gives -1 so it will have a maximum (similar to a normal modulus of the form -|x|)

        regards
        J

  2. And what is that “little thought” which will tell us at which end the minimum will lie ? I’m asking this so that I can have an idea of the graph without even plotting it. (might help other types of questions)
    If that’s confusing then leave it 😛

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