2 + (1+1+1) = 5 - 100 followers problem

Algebra Level 5

Statement 1

$\left[ x+\frac { 1 }{ 2 } \right]$ is an odd function, while $\cos { \pi x }$ is an even function.

Statement 2

$\left[ x+\frac { 1 }{ 2 } \right] \cos { \pi x }$ is an odd function.

Statement 3

Product of an odd function and an even function is an odd function.

$[x ]$ is the greatest integer less than or equal to $x$ .

Both Statement 1 and Statement 2 are correct but Statement 3 is not the correct explanation. Statement 2 is incorrect, while Statement 1 is correct. Both Statement 1 and Statement 2 are correct and Statement 3 is the correct explanation. Both Statement 1 and Statement 2 are incorrect. Statement 1 is incorrect but Statement 2 is correct.

1 solution

Geoff Pilling
May 18, 2017

Statement one is incorrect since $f(\frac{1}{2}) = 1$ , but $f(-\frac{1}{2}) = 0$ .

(Where $f = [x+\frac{1}{2}]$ )

However, since the only place where that inconsistency exists is at $\dfrac{n}{2}$ for odd $n$ , and $cos(\pi x)$ is zero at those values, the second statement is true.

Bye the way, it looks like its now time to post a "200 follower" problem! :0) Congrats!

2 + (1+1+1) = 5 - 100 followers problem

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