COMPOSITE FUNCTIONS - range dilemma

Question

The function F is defined for all non-negative values of x by

                             1/2

F(x) = 3 + x        ( that is 3 + square root of x )

Evaluate ff(169).

F(169) = -10 or 16   I discard the -10 as domain is only for +ve x

FF(169) then is F(16) = -1 or 7.

Now the official answer is 7 without any mention of the -1.

1)  Is this elimination of the -1 in the answer because F is defined as a function and thus cannot strictly have 2 elements in the range mapped from one element in the domain or ............

2) because this composite function involves using and element from the range as the new element of the domain for the second iteration ? If this is the reason I do not understand because there in no third iteration of re-entering the answer.

HELP ?!

 

 

 

 

 

Answer 1

This query can be closed now as I understand that the range of the inner function has to form the domain of the outer function.

Thank you.

Answer 2

Con you help me find answer??  let f(x)= 4x-1, h(x)= -x+3. find (hof)(4)