Answer:
The statement is false as it depends on the domain
Step-by-step explanation:
We are given the statement,
For a trigonometric function \(y=f(x)\) implies \(x=f^{-1}(y)\).
This statement is not always true.
For example,
The function \(y=\sin x\) is one-one and onto in the domain \([-\frac{\pi}{2},\frac{\pi}{2}]\).
Thus, its inverse exists in \([-\frac{\pi}{2},\frac{\pi}{2}]\).
That is, in \([-\frac{\pi}{2},\frac{\pi}{2}]\), \(y=\sin x\) implies \(x=\sin^{-1}(y)\).
Hence, we see that,
It depends on the domain for the given statement to be true.
Thus, the statement is false.
