Question

True or false (precalculus)?

Answer 1

For a trigonometric function, y = f(x), then x = F^-1(y).

Answer 2

In order for a function to have an inverse,
it must be `one-to-one`.
Meaning: It must pass the `horizontal line test`.

Answer 3

So this is false, because it is not always true?

Answer 4

So think about your crazy squiggly graphs...
and whether or not that holds true.

Answer 5

You're right, it's false.
It's false because the trig functions are `periodic`, ya?
They repeat y values over and over.

Answer 6

yea - like the sine curve which is a repeating wave

Answer 7

But there's such a thing as inverse trig functions... how come?

Answer 8

Ah that's a great question! :)

If you take your sine function for example,
and restrict it to `one full period` in a careful way,then it will pass the horizontal line test, ya? :)