1980 AHSME Problems/Problem 14
Revision as of 11:48, 5 July 2013 by Nathan wailes (talk | contribs)
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 .
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
