Which of the Following functions is the inverse of fx cos x

Which of the Following functions is the inverse of f(x) = cos x restircted to the interval [0,pi]

a. g(x) = sec(x) with domain [0,pi] and range [-1,1]   

b. g(x) = cos(x) with domain [0,pi] and range [-1,1]

c. g(x) = cos(x) with domain [-1,1] and range [0,pi]

d. g(x) = cos^-1 (x) with domain [-1,1] and range [0,pi]

e. g(x) = cos^-1 (x) with domain [0,pi] and range [-1,1]

f. g(x) = sec(x) with domain [-1,1] and range [0,pi]

Solution

f(x) = cosx

Domain: [ 0, pi ] ; range : [ 1, -1 ]

Inverse : y = cosx

x= cosy

y = cos^-1(x)

Domain: [ -1, 1 ]

Range ;[ 0, pi]

Option d