Question

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

Can someone help me please?

Answer 1

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

Answer 2

The statement is false as it depends on the domain

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
`[-(\pi)/(2),(\pi)/(2)]`.

Thus, its inverse exists in
`[-(\pi)/(2),(\pi)/(2)]`.

That is, in
`[-(\pi)/(2),(\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.