Question

True or false. For a trigonometric function, y=f(x) then x=F-1(y). Explain your answer.

Answer 1

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.

Answer 2

False if y=f(x) then x= inverse of f(x) or f^-1(x)