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