Let \( f: R \rightarrow R \) defined by \( f(x)=\cos ^{-1}(-\{-x\}) \), where \( \{\mathrm{x}\} ...

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Let \( f: R \rightarrow R \) defined by \( f(x)=\cos ^{-1}(-\{-x\}) \), where \( \{\mathrm{x}\} \) is fractional part function. Then which of the following is/are correct?
(a) \( f \) is many-one but not even function
(b) Range of \( f \) contains two prime numbers
(c) \( f \) is a periodic
(d) Graph of \( f \) does not lie below \( x \)-axis
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