Continuity of a composite function
Suppose the function Theorem 8. Suppose the function Theorem 9 (of continuity of an inverse function). Suppose the function
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Continuity of a composite function
Suppose the function Theorem 8. Suppose the function Theorem 9 (of continuity of an inverse function). Suppose the function
|
is defined in the multitude X, and Y is a range of this function. Suppose the function 
is defined in the multitude Y. Then they say, that in the multitude X a composite function is defined. It is written as 
.
. Then the composite function 
is continuous at point a.
is defined, monotonically increasing (decreasing) and continuous on some interval X. Then on the respective interval Y of the range of this function a simple inverse function 
exists, which is also monotonically increasing (decreasing) and continuous.
