Question

Which of the following are inverse functions?

1. Arcsin x and sin x
2. cos^-1 x and cos x
3. csc x and sin x
4. e^x and ln x
5. x^2 and +/- sqrt x
6. x^3 and cubic root of x
7. cot x and tan x
8. sin x and cos x
9. log x/3 and 3^x

I believe the answers are 2, 4, 6, and 9, but how come not the rest, especially csc/sin and cot/tan?

Thank you very much!

Answer 1

pick any x
perform the first operation
perform the second operation on that answer.
did I get back the original x ?

cscx and sinx, cotx and tanx are reciprocal functions, not inverses

my choices of inverse are:
1,2,4,6

(how did you figure #9 represents an inverse ???)