What is the range of the function defined by 
?
Select an Answer
All real numbers
All real numbers except 
All real numbers except 0
All real numbers except 2
All real numbers between 2 and 3
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The correct answer is D.
The range of the function defined by is the set of 
such that 
for some 
.
One way to determine the range of the function defined by is to solve the equation for 
and then determine which correspond to at least one . To solve for , first subtract 
from both sides to get 
and then take the reciprocal of both sides to get 
. The equation shows that for any 
other than , there is an such that , and that there is no such for 
. Therefore, the range of the function defined by is all real numbers except .
Alternatively, one can reason about the possible values of the term 
. The expression can take on any value except 
, so the expression 
can take on any value except . Therefore, the range of the function defined by is all real numbers except .