Home > Precalculus > Function Composition

Is it always true that #(f@g)(x) = (g@f)(x)#?

Answer 1

Ariana Alvarez

This relationship is true only if the functions #f# and #g# are inverse functions of each other.

Please see the video.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Serenity Johnson

No, it is not always true that ((f@g)(x) = (g@f)(x)). The equality depends on the definitions of the operations (f@g) and (g@f). If (f) and (g) are functions and (@) denotes a binary operation such as composition, then generally ((f \circ g)(x) \neq (g \circ f)(x)) because the order in which functions are applied can affect the outcome.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.