Example 18 - Show that if f, g are one-one, then gof is one-one

Example 18 - Chapter 1 Class 12 Relation and Functions - Part 2

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 2 Show that if f : A → B and g : B → C are one-one, then gof : A → C is also one-one. Checking gof one-one We need to prove that If gof (x1) = gof (x2), then x1 = x2 Suppose gof (x1) = gof (x2) g (f (x1)) = g(f (x2)) Given g is one-one So, f (x1) = f (x2), And f is also one-one x1 = x2 Hence, gof is one-one.

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.