MHB Why Does Subtraction Become Addition in Composite Functions?

AI Thread Summary
In the discussion on composite functions, the focus is on understanding why subtraction appears as addition in certain transformations. The example provided involves calculating g(-1) for the function g(x) = -4x² - 5x. It clarifies that subtracting a number can be expressed as adding its negative, which is a fundamental property of arithmetic. This transformation can lead to confusion, but both representations are mathematically equivalent. The explanation emphasizes the importance of recognizing this principle in composite function calculations.
mitchconnor
Messages
2
Reaction score
0
g(x)=−4x2−5x
f(x)=−3x2+7x−5(g(x))

f(g(−1))=?

First, let's solve for the value of the inner function, g(−1). Then we'll know what to plug into the outer function.

g(−1)=−4(−1)2+(−5)(−1)I don't understand why they transformed the minus symbol into an addition symbol. This has happened a few times now. Every time I think I get an answer, I get hoodwinked by this change!

Help would be much appreciated.
 
Last edited:
Mathematics news on Phys.org
Re: Composite function troubles~

Note that:

$$-4(-1)^2+(-5)(-1)=-4(-1)^2-5(-1)$$

I would choose to write it they way it is on the right, but both are equivalent. It boils down to the fact that subtracting a number is the same as adding the negative of that number:

$$a-b=a+(-b)$$
 
Last edited:
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top