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Answer:
- f(x) = x
- g(x) = -2x+1
- f(x) -(-g(x)) = -x+1
- f(x) +g(x) = -x+1
- f(x)-(-g(x)) = (f+g)(x) is true for all functions f and g, linear or not
Step-by-step explanation:
We can define a couple of linear functions as ...
f(x) = x
g(x) = -2x+1
Then the reflected function -g(x) is ...
-g(x) = -(-2x +1) = 2x -1
And the difference from f(x) is ...
f(x) -(-g(x)) = x -(2x -1) = -x +1 . . . . f(x) -(-g(x))
We want to compare that to the sum of the functions:
f(x) +g(x) = x +(-2x +1) = -x +1 . . . . f(x) +g(x)
The two versions of the function expression have the same value.
These results are <em>a property of addition</em>, so do not depend on the nature of f(x) or g(x). They will hold for every function.
