just a quick question. When trying to determine the zeros of a function and you are finding the negative real zeros, how exactly to you write the function f(-x). Like what i mean is how do you know which signs need to be changed?

Question

jdoe0001 · Answer

ahemmm, well, you'd want to change all "x" to "-x"
and it makes it easier to avoid confusion if you enclose them in parentheses

anonymous · Answer

For example with these three equations i have.

$$f(x)=x^3-3x^2-16x+48$$
$$f(x)=x^3-12x^2+28x-9$$
$$f(x)=x^4-x^3+7x^2-9x-18$$

jdoe0001 · Answer

say f(x) = 2x^3+x^2

f( -x ) = 2(-x)^3 + (x)^2

-x * -x * -x = (-x)^3 
-x * -x * -x = -x^3

-x * -x = (-x)^2
-x * -x = x^2

f( -x ) = -2x^3 + x^2

jdoe0001 · Answer

the rule goes, if the exponent is ODD, on the -x it will change sign
due to the unevenness of the sign multiplication

if the exponent is EVEN, it will end up as positive
same reason, due to the evenness of the sign multiplication

- * - * - = -
-* - = +

anonymous · Answer

oh okay thank you(:

jdoe0001 · Answer

yw

anonymous · Answer

One thing. for like the first equation i put, $$f(x)=x^3-3x^2-16x+48$$ does it become $$f(-x)==x^3+3x^2+16x+48$$

anonymous · Answer

And the second one from $$f(x)=x^3-12x^2+28x-9$$ to $$f(-x)=-x^3+12x^2-28x-9$$

anonymous · Answer

And the last one from $$f(x)=x^4-x^3+7x^2-9x-18$$ to $$f(-x)=x^4+x^3+7x^2+9x-18$$

anonymous · Answer

@jdoe0001 ?