Question

The inverse of the function f(x)=sin(4⋅x+3)  is  f−1(x)=
(a) csc 4⋅(x+3)
(b) arcsin 4⋅(x+3)
(c) arcsin (x−3)/4
(d) arcsin ((x)−3)/4
(e) arcsin (x−3)/4

Answer 1

y = sin(4x + 3)
4x + 3 = arcsin y
4x = arcsin y - 3
x = (arcsin y - 3)/4

Inverse => f^-1(x) = (arcsin(x) - 3)/4