- #1
irvin.b
- 2
- 0
i really need to see the proof of this theorem:
if f and g are bijective then the inverse of (g o f) = inverse of f o inverse of g
if f and g are bijective then the inverse of (g o f) = inverse of f o inverse of g
A composite function inverse is a mathematical concept that refers to the inverse of a function that is composed of two or more other functions. It represents the original function "undoing" the effects of the composite function.
The inverse of a composite function can be found by first finding the inverse of each individual function within the composite function and then composing them in reverse order.
The domain of a composite function inverse is the range of the original composite function. This is because the inverse function "undoes" the effects of the composite function, so any input values that were originally mapped to a particular output value will now be mapped back to that same input value.
Yes, the original composite function must be one-to-one, meaning that each input value is mapped to a unique output value. If the original function is not one-to-one, then its inverse will not exist.
No, a composite function can only have one inverse. This is because the inverse function must also be one-to-one, and if there were multiple inverse functions, then the input values would not be mapped to a unique output value.