Find the inverse function f1 of the function f Find the rang

Find the inverse function f^-1 of the function f. Find the range of f and the domain and range of f^-1. f(x) = -7 cos (6x); 0 x pi/6

f(x) = -7cos(6x) for 0< = x< = pi/6

range of f(x) = 7*[-1,1] = [ -7, 7 ] ( range of cos function is [-1, 1] )

y = -7cos(6x)

Plug x= y and y =x and solve for y :

x = -7cos(6y)

(-x/7) = cos6y----> y = (1/6) cos^-1(-x/7)

f^-1(x) =(1/6) cos^-1(-x/7)

Domainof f^-1(x) is the range of f(x) = [ -7,7 ]

Range is equal to domain of f(x) = [ 0, pi/6 ]