Finding invertible complex function

[gzAbc123]

Hi there,
This is my first time posting on this site. I'm doing Calculus 2 and am stuck on finding whether or not the following functions are invertible in the given intervals and explaining why.

(a) sechx on [0,infinity)

--> I solved (a) but (b) and (c) is where I'm stuck.

(b) cos(lnx) on (0, e^pi)

(c) e^(x^2)

Can someone please help?

 

[quantumdude]

You don't have to find the inverse function, you just have to determine if an inverse exists. A necessary condition for invertibility on an interval is that the function is one-to-one on that interval. This condition is met if the function is monotonic on the interval.

So how would you determine whether a function is monotonic on $[0,\infty)$?

 

[mancini0]

A function is monotonic if it is strictly increasing or decreasing, correct? Then one would find this info out based on the sign of the first derivative?