1980 AHSME Problems/Problem 14
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As , we can plug that into
and simplify to get
. However, we have a restriction on x such that if
we have an undefined function. We can use this to our advantage. Plugging that value for x into
yields
, as the left hand side simplifies and the right hand side is simply the value we have chosen. This means that
, which is answer choice A.
Alternatively, after simplifying the function to , multiply both sides by
and divide by
to yield
. This can be factored to
. This means that both
and either one of
or
are equal to 0.
yields
and the other two yield
. The clear solution is
.