Here is some good news: All linear functions, are bijections.
In part b) look at the derivative.
For the others, find counter examples.
Determine whether or not the following functions from real numbers to real numbers are bijections (I don't need help with this part), and explain why or why not (I need help with THIS part).
a) (Bijective)
b) (Bijective)
c) (Bijective)
d) (Not bijective)
e) (Not bijective)
The main issue I'm having with this problem is proof presentation. I don't exactly know how to explain whether or not a function is bijective or not.
Of course, if I've made a mistake, I'd appreciate it if you let me know.
Thank you both for your answers. Looking at this again, however, I'm wondering how I'd prove how the fourth one is not bijective, mainly since it's an absolute function.
I actually can't find a situation where . Anyone have a suggestion so I can prove that it's not injective, and therefore not bijective?