Answer:
x = ⅓ acos(y/7) + π/18, [-7, 7/2]
Step-by-step explanation:
y = 7 cos(3x − π/6)
Solving for x:
y/7 = cos(3x − π/6)
acos(y/7) = 3x − π/6
acos(y/7) + π/6 = 3x
x = ⅓ acos(y/7) + π/18
The domain of x is the same as the range of y.
When x = π/6:
y = 7 cos(3π/6 − π/6)
y = 7 cos(π/3)
y = 7/2
When x = 7π/18:
y = 7 cos(21π/18 − π/6)
y = 7 cos(π)
y = -7
So the domain of x as a function of y is [-7, 7/2].
