Real functions, imaginary inputs

Algebra Level 3

For some x R x \in \mathbb{R} , which of the following are real functions?

  1. sin ( i x ) \sin{(ix)}
  2. cos ( i x ) \cos{(ix)}
  3. tan ( i x ) \tan{(ix)}
  4. sinh ( i x ) \sinh{(ix)}
  5. cosh ( i x ) \cosh{(ix)}
  6. tanh ( i x ) \tanh{(ix)}
  7. arcsin ( i x ) \arcsin{(ix)}
  8. arccos ( i x ) \arccos{(ix)}
  9. arctan ( i x ) \arctan{(ix)}

Concatenate the number(s) of the function(s) that are real functions in ascending order and submit that as your answer. For example, if functions 1 , 2 , 3 , 4 , and 5 are real functions, then your answer should be 12345 . If you think that none of these functions is a real function, input your answer as 0 .


Notation: i = 1 i = \sqrt{-1} denotes the imaginary unit.


The answer is 25.

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