Question

Let f(x) = cos^-1 x. Then the domain of f(x) is all real numbers and the range is [-1,1]. Is this true or false?

Answer 1

It's false.

Answer 2

why?

Answer 3

\[
\cos : \mathbb{R}\mapsto [-1,1]
\]\[
\cos^{-1} :[-1,1]\mapsto \left[\frac{-\pi}{2},\frac{\pi}{2}\right]
\]

Answer 4

what about if f(x) was tan^-1x then the domain(x) is all real numbers and the range was [0,pi], would in this case it be true?