For the function `f(x) = cos^(-1)x + cos ^(-1) x^(2)` which of the following statements is/are true

The function,f(x)=cos^(-1)(cos x) is

Let f(x)=sin^(-1)x and g(x)=cos^(-1)x , then which of the following statements are correct?

For the function f(x)=x "cos" 1/x, x ge1

For the function f(x)=x cos((1)/(x)),x>=1

For tha function f(x)=(pi-x)(cos x)/(|sin x|);x!=pi and f(pi)=1 which of the following statement is/are true:

Range of the function f(x)=(cos^(-1)abs(1-x^(2))) is

Let f(x)=sqrt((cos^(-1)sqrt(1-x^(2))-sin^(-1)x)) then which of the following statement/s is are correct -