Consider the function f (x) = ^ -1 ( [ 3 ^ x ]) + ^ -1 ([ 3 ^ x ] -...

For $f \left(x\right)$ to be defined \left[{3}^{x}\right] =0, 1$<br /><br />$∴ {3}^{x} \in \left[0, 2\right) ⇒ x \in \left(- \infty, \log_{3} 2\right)$<br /><br />Range of$f\left(x\right)= \left\{\cos^{- 1} \left(0\right) + \sin^{- 1} \left(-1\right), \cos^{- 1} \left(1\right) + \sin^{- 1} \left(0\right)\right\} ≡ \left\{0\right\}$<br /><br />$∴ f\left( x\right) = 0 \forall x \in \left(- \infty, \log_{3}2\right)

So, the domain is not symmetric about the origin

∴ f \left( x\right)& is neither even nor odd