# Thread: How to know when the substituted variable is going to be negative or positive

1. ## 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!

2. ## 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:

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

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.

3. ## 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!

4. ## Re: How to know when the substituted variable is going to be negative or positive

In my post, $\displaystyle \cdot$ 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,

$\displaystyle -3^4 = -(3^4) = -81$
$\displaystyle (-3)^4 = 81$

This is solely a matter of notation, just making sure the reader knows exactly what we are trying to say.