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
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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.
 
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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:

$$a-b=a+(-b)$$
 
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