Show that if and are monotonically increasing functions, then so are the functions and , and if and ) are in addition nonnegative, then is monotonically increasing.

As and are monotonically increasing functions,

Therefore, , i.e. is monotonically increasing.

Also, combining (1) and (2), Therefore, is also monotonically increasing.

If and ) are nonnegative then combining this new information with (a) and (2), we can say:

Therefore, is monotonically increasing.

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