Question

50 POINTS!!!

Answer 1

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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 a property of addition, so do not depend on the nature of f(x) or g(x). They will hold for every function.