I'm definitely not a math person and only did general mathematics in high school, and unfortunately, not paying as much attention to that as I should have.
Well, I'm doing Discrete Mathematics in my degree and I'm working through solving composite functions.
I've noticed that people tend to bring over a negative, in brackets, and then add them... I know that doesn't make sense, I'll explain:
Assume the following:
$ h(t) = t^2 -2t $
$ g(x) = -6x^2 - 6x - 7 - 5(h(x)) $
$ g(h(1)) = ? $
So, with regards the above, my working is:
$ h(1) = 1^2 - 2 * 1 = -1 $
$ g(-1) = (-6)(-1)^2 - (6)(-1) - 7 - 5(h(-1)) $
$ h(-1) = (-1)^2 - (2)(-1) = 3 $
$ g(-1) = (-6)(-1)^2 - (6)(-1) - 7 - 5(3) $
$g(-1) = -22 $
However, in the example working provided, they do:
$ h(1)=1^2+(−2)(1) $
$ h(1) = -1 $
$ g(−1)=−6(−1)^2 +(−6)(−1)−7−5(h(−1)) $
$ h(-1) = (-1)^2 + (-2)(-1) $
$ h(-1) = 3 $
$ g(-1) = −6(−1)^2 +(−6)(−1)−7+ (-5)(3) $
I don't know why they add the negatives 7 + (-5)(3), where it could more easily be written 7 - (5)(3).
I don't know what this principle is called (what is it?), and as such, I don't know why this rule applies. My friend told me I would lose marks if I work out equations my way, and as such, I'd like to do this the "correct" way.
Could anyone please explain (remembering my lesser math background)?
Thanks.
Here's my best shot at explaning what's going on:
They "add the negatives" in $-7 + (-5)(3)$ because subtraction is the inverse of addition. Subtracting a number $b$ from $a$ ($a - b$) is also adding $b$'s additive inverse to $a$ ($a + (-b)$). However, your method is indeed correct because it follows what the problem is saying. They must've added parentheses. You would just drop them and continue to solve. It still ends up with the same answer.