So, Im studying limits, and got to the incredible cool intermediate value theorem now, and found this question in my book. Even though he doesnt ask for THE number, he wants me to show that it exists, so i tried:

$\displaystyle x = x³ + 1$

now, here is where the problem stats, i can form two different functions,

$\displaystyle f(x) = x³ + 1 - x$

$\displaystyle g(x) = -x³ - 1 + x$

By testing, however, the answer is the same, x is in $\displaystyle (-1,4 , -1,3)$. But when I actually look at the results, I notice that:

$\displaystyle f(-1,3) = 0,103 $

$\displaystyle g(-1,3) = -0,103$

$\displaystyle f(-1,4) = -0,344$

$\displaystyle g(-1,4) = 0,344$

Even though in this case the function I choose wont matter, since I will get to the answer, Should I have picked one over another?