Professor Kate Poirier, Spring 2017

Author: Javed

Test #2 Solutions Question 2a


a) Determine whether f is invertible. If f is invertible, find it’s inverse f^-1. Explain your answer.

f(x) = 2x+1 is one-to-one

f^-1(x) = (x-1)/2


(f^-1 o f)(x) = (2x + 1 – 1) / 2

= 2x/2

= x

(f o f^-1)(x) = 2 ((x-1)/2) + 1

= x – 1 + 1

= x

If f: f -> f^-1 is one-to-one, it is invertible. It’s inverse f^-1 is the function f^-1:f^-1 o f such that f -> f^-1 o f -> f^1 and f^-1 -> f o f^-1 -> f are identify functions.

Introduction Javed


I’m a transfer student and this is my second semester here at City Tech. My major is in computer systems focusing on networking and security. I started doing programming, but wasn’t as enthusiastic about it and switched over to network where I’m enjoying it more. I’ve always been into computers since my dad worked in the field doing networking, so I was exposed to it at an early age.  I’ve already learned a lot about this field from him making it an easy decision when selecting my major. After graduating from here, I hope to work in the networking field as a network administrator. If that doesn’t work out, the security field is also very good. I hope to fully understand algorithms and mathematical logic since it is the bases of computer programming, at the end of the semester. During my free time, I like working on computers and building them. I’ve built many for friends and family so they can have a better computer and not spend so much on it. I also enjoy writing programs for fun. It helps me get better at coding and I just find it fun.