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
View Correct Answer
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
.