Question

Under which conditions does the commutative property apply to compositions of f(x) and g(x)? A- When they are inverse functions B- when they are equal for at least one value of x C- when they are equal for all values of x D- when they are not inverse functions

Answer 1

Answer:

  A- When they are inverse functions

  C- when they are equal for all values of x

Step-by-step explanation:

The order of function application in a composition can be reversed if ...

• the functions are inverses of each other
• the functions are identical (equal for all values of x)

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In the first case, the composition gives an output equal to its input for the functions in either order.

In the second case, you cannot tell the functions apart, since they produce the same output for the same input. Hence, you can't tell if they are reordered or not.