Answer:
y = 4 - sin⁻¹x
Step-by-step explanation:
1. Reflection about y = x
If we reflect a function ƒ(x) about the line y = x, we are creating its inverse, ƒ'(x).
Thus, reflection of y = sinx about y = x gives y = sin⁻¹x.
The range of the reflection extends from -∞ to +∞, but the range of the function y = sin⁻¹x is [-π/2, π/2] (see Fig. 1)
.
2. Reflection about y = 2
Reflection about y = 2 retains the sign of x but changes the sign of y.
Note, however, that in Figure 2 the point at (0, 0) is reflected to (4, 0).
The function is translated up by four units.
After the two reflections, the equation of the line is
y = 4 - sin⁻¹x
