Difference between revisions of "1995 AHSME Problems/Problem 12"
(New page: ==Problem== Let <math>f</math> be a linear function with the properties that <math>f(1) \leq f(2), f(3) \geq f(4),</math> and <math>f(5) = 5</math>. Which of the following is true? <math...) |
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Revision as of 10:00, 9 January 2008
Problem
Let be a linear function with the properties that
and
. Which of the following is true?
Solution
A linear function has the property that either for all a<b, or for all b<a. Since
,
. Since f(1)\leq f(2)
f(1)=f(2)
f(a)=f(b)$for a≠b, then f(x) is a constant function. Since$ (Error compiling LaTeX. Unknown error_msg)f(5)=5
f(0)=5\Rightarrow \mathrm{(D)}$