posted by Veronica .
Having trouble with true/false questions in Trigonometry. They read as follows -
True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer.
True or False: For a one to one function, y=f(x), then x=f^-1(y). Explain your answer.
True or False: For any function, x=f^-1, then y=f(x). Explain your answer.
In the lesson, we were taught that for inverses, capitals, F, denote inverse functions, and lowercase, f, denote inverse relations. From the info taught to me, I have these answers:
1 - False (The domains and ranges of inverse trig functions, F, are restricted)
2 - True (Since the function is one-to-one, there is no chance of the original function going over the allowable domain of the inverse)
3 - I believe that this is true, since x = f^-1(y) is a relation (lowercase).
I wanted to make a bit of a correction, for my third answer, the x = f^-1(y) is specified as a function (as seen above). But wouldn't this still be true?