The inverse of cosine function is defined in the intervals

Inverse function

Verify Rolle's Theorem for the functions : f(x)=cosx , defined in the interval [-pi/2,pi/2]

The function sin^(-1)sqrt(x) is defined in the interval

Verify Rolle's Theorem for the functions : f(x)=tanx , defined in the interval [0,pi] .

The function f(x) is defined on the interval [0,1]. Find the domain of definition of the functie f(sin x)

Verify Rolle's Theorem for the functions : f(x)=sin^(2)x , defined in the interval [0,pi]

The function f(x) is defined on the interval [0,1]. What are the domains of definition of functions. (a) f(sin x), (b) f(2x+3)?