Range Of A Function

The function $y%20%3D%20%5Csin%5E%7B-1%7Dx$ is the inverse sine function.

Its domain is: $%5B-1%2C%201%5D$
Its range is: $%5Cleft%5B%20-%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%5Cright%5D$

In the given problem, the domain is restricted to: $-1%20%5Cleq%20x%20%5Cleq%200$

At $x%20%3D%20-1$ , $y%20%3D%20%5Csin%5E%7B-1%7D(-1)%20%3D%20-%5Cfrac%7B%5Cpi%7D%7B2%7D$
At $x%20%3D%200$ , $y%20%3D%20%5Csin%5E%7B-1%7D(0)%20%3D%200$

Since the inverse sine function is continuous and strictly increasing, the range of $y$ is:

$%5Cleft%5B%20-%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%200%20%5Cright%5D$

Correct Answer: $%5Cboxed%7B%20%5Cleft%5B%20-%5Cfrac%7B%5Cpi%7D%7B2%7D%2C%200%20%5Cright%5D%20%7D$

Chapter Questions
1 MCQs