1975 AHSME Problems/Problem 21
Problem
Suppose is defined for all real numbers
for all
and
for all
and
. Which of the following statements are true?
Solution
Let . Our equation becomes
, so
. Therefore
is always true.
Let . Our equation becomes
. Therefore
is always true.
First let . We get
. Now let
, giving us
. Therefore
is always true.
This is false. Let
, for example. It satisfies the conditions but makes
false. Therefore
is not always true.
Since are true, the answer is
.
See Also
1975 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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