Let f ( x ) = x − ⌊ x ⌋ , x  = 0 . How many solutions satisfy f ( x ) + f ( 1/ x ) = 1 ?

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MathematicsFunctionsPeriodicityHard3 minQB

MathematicsHardsingle choice

Let $f (x) = x - ⌊ x ⌋, x \neq = 0$ . How many solutions satisfy $f (x) + f (1/ x) = 1$ ?

Answer:

Solution:

This is equivalent to $x + 1/ x$ being an integer except ±2; infinitely many integers work.

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Periodicity

⏱ 3mℹ️ Source: QB

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