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Math Help - How to know when the substituted variable is going to be negative or positive

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    Senior Member sakonpure6's Avatar
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    How to know when the substituted variable is going to be negative or positive

    Hi, i am a bit confused about the positive/negative value of numbers when they are substituted.

    Q1. X^2+y^2=25 the points can be negative and positive but the question is when do you put brackets around those negative numbers because sometimes we sub them in without brackets?

    Q2. F(x)=x^2 now i know f(2x) = 4x^2 but how about f(-2x) would it be the same?

    I would be glad if someone can clear those things for me!

    Have a nice day!
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    Re: How to know when the substituted variable is going to be negative or positive

    Sorry I didn't understand your first question... Which points? Can you rephrase it? =/

    For Q2, yes this would be correct. You can verify it like this:

    (-2x)^2 = (-2)^2 \cdot x^2 =4 \cdot x^2 = 4x^2

    Also, x^2 is an even function, f(x) = f(-x), therefore, changing the sign of the input variable won't change the function value.
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    Senior Member sakonpure6's Avatar
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    Re: How to know when the substituted variable is going to be negative or positive

    what does the dot mean in your equation, (im only gr.11) and for Q2.

    Equation of a circle,for example x^2+y^2=25. Some (x,y) points that belong to the equation can be (1,5) and (-1,-5) and in this case when sub-ing in (-1,-5) we put brackets around them. But in some cases we do not(I believe so). I want to know why and when do we put brackets around negative numbers when substituting them in for variables.

    Thanks!
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    Re: How to know when the substituted variable is going to be negative or positive

    In my post, \cdot means multiplication.

    You need parentheses when order of operations requires them.. for example, If you want to evaluate x + 2, and x = -2, you don't need them because -2 + 2 = 0 and there's no confusion as to what this means. But it would totally be correct if you included them regardless.

    But when you are plugging a number into x^4, and the number is negative, you need parantheses, because for x = -3:

    -3^4 would mean the same thing as -(3^4), since exponents are evaluated first, just due to the notation. This is NOT what we want, so we need to put parentheses around (-3) to make clear that it is one number. In this case,

    -3^4 = -(3^4) = -81
    (-3)^4 = 81

    This is solely a matter of notation, just making sure the reader knows exactly what we are trying to say.
    Last edited by SworD; September 12th 2012 at 06:19 PM.
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