If $f\left(x\right)={\sin }^{-1}x.{\cos }^{-1}x.{\tan }^{-1}x.{\cot }^{-1}x.{\sec }^{-1}x.\cos e{c}^{-1}x,$ then which of the following statement(s) hold (s) good?

The graph of $y=f\left(x\right)$ does not lie above x axis

The non-negative difference between maximum and minimum value of the function $y=f\left(x\right)is\frac{3{\pi }^6}{64}$

The function $y=f\left(x\right)$ is not injective

Number of non-negative integers in the domain of  $f\left(x\right)$ is two