Find the inverse function f1 of the function f f x 3 sin x

Find the inverse function f^-1 of the function f. f (x) = 3 sin x - 6 Find the domain of the function f and of its inverse function f(x) = -7 cos(10x) Find the exact solution of the equation. -sin^-1(4x) = pi/4

Solution

f(x) = 3sinx - 6

Let f(x) = y

y = 3sinx - 6

interchange x and y

x = 3siny - 6

=> siny = (x+ 6)/3

=> y = sin^-1[(x+ 6)/3]

=> f^-1(x) = sin^-1[(x+ 6)/3]