1985 AHSME Problems/Problem 23
Contents
Problem
If where , then which of the following is not correct?
Solution 1
We can write which gives using the fact that is an even function and is an odd function.
Accordingly, and upon substituting the values from the answer choices, we find that for all such values except , where . Thus the answer is .
Solution 2
Notice that and , so and hence . Similarly, and
Now let . Then, using the results and from above, we obtain
Again from above, and , so giving . Similarly, giving , meaning that the answer must be . To confirm this, we further note that giving , and finally giving , which shows that the only false statement is indeed .
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
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