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 .
- mako17
See Also
1975 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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