Question

Are the functions commutative or not commutative.
1. f (x) = 1/4x + 5 g (x) = 4x - 20

2. f (x) = 2x + 4 g (x) = x^2 - 3


Please show steps.

Answer 1

Answer:

1. commutative
2. not commutative

Step-by-step explanation:

1. The functions in a composition will be commutative if they are inverses of each other.

  f(g(x)) = 1/4(4x-20) +5 = x -5 +5 = x

  g(f(x)) = 4(1/4x +5) -20 = x +20 -20 = x

The functions f and g are inverses of each other and are commutative. Application of these functions in either order will give the same result--the original function's argument.

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2. f(g(x)) = 2(x^2 -3) +4 = 2x^2 -2

   g(f(x)) = (2x +4)^2 -3 = 4x^2 +16x +13

f(g(x)) gives a different result than g(f(x)), so the functions are not commutative.