Question

use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function: f(x) = cos(3x/2)

Answer 1

is there a particular restriction on the domain for this function? otherwise you should observe that any sinusoidal function is periodic

Answer 2

no, no restrictions,

Answer 3

I think I am suppose to start with the derivative, but I'm not sure.

Answer 4

the cosine function is wavy and hence not monotonic on its entire domain. taking a derivative isn't required to come to this conclusion but you could take the derivative and say the same thing about its derivative.

Answer 5

monotonic just means 'always increasing' or 'always decreasing'. but the cosine function oscillates so it decreases sometimes, then increases, then decreases, etc., etc. so it is not monotonic.

but if you must take a derivative, you can. but you will get a function in terms of sin. and the same conclusion can be drawn.

Answer 6

ah ok, that makes sense. Thank you.