
Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at Sept. 25, 2018 by Teachoo
Transcript
Example 9 Prove that the function f : R → R, given by f (x) = 2x, is one-one and onto. f(x) = 2x Checking one-one f (x1) = 2x1 f (x2) = 2x2 Putting f(x1) = f(x2) 2x1 = 2 x2 x1 = x2. Hence, if f(x1) = f(x2) , x1 = x2 ∴ function f is one-one Onto f(x) = 2x Let f(x) = y, , such that y ∈ R 2x = y x = 𝑦2 Since y is a real number, Hence 𝑦2 will also be a real number So, x will also be a real number, i.e., x ∈ R Hence, f is onto
Examples
Example 2
Example 3
Example 4 Important
Example 5
Example 6 Important
Example 7
Example 8
Example 9 You are here
Example 10
Example 11 Important
Example 12 Important
Example 13 Important
Example 14 Important
Example 15 Not in Syllabus - CBSE Exams 2021
Example 16 Not in Syllabus - CBSE Exams 2021
Example 17 Not in Syllabus - CBSE Exams 2021
Example 18 Important Not in Syllabus - CBSE Exams 2021
Example 19 Important Not in Syllabus - CBSE Exams 2021
Example 20 Not in Syllabus - CBSE Exams 2021
Example 21 Not in Syllabus - CBSE Exams 2021
Example 22 Not in Syllabus - CBSE Exams 2021
Example 23 Important Not in Syllabus - CBSE Exams 2021
Example 24 Not in Syllabus - CBSE Exams 2021
Example 25 Important Not in Syllabus - CBSE Exams 2021
Example 26 Not in Syllabus - CBSE Exams 2021
Example 27 Important Not in Syllabus - CBSE Exams 2021
Example 28 Not in Syllabus - CBSE Exams 2021
Example 29 Not in Syllabus - CBSE Exams 2021
Example 30 Not in Syllabus - CBSE Exams 2021
Example 31 Not in Syllabus - CBSE Exams 2021
Example 32 Not in Syllabus - CBSE Exams 2021
Example 33 Not in Syllabus - CBSE Exams 2021
Example 34 Not in Syllabus - CBSE Exams 2021
Example 35 Not in Syllabus - CBSE Exams 2021
Example 36 Not in Syllabus - CBSE Exams 2021
Example 37 Not in Syllabus - CBSE Exams 2021
Example 38 Not in Syllabus - CBSE Exams 2021
Example 39 Not in Syllabus - CBSE Exams 2021
Example 40 Not in Syllabus - CBSE Exams 2021
Example 41 Important
Example 42 Important
Example 43 Important
Example 44
Example 45 Important Not in Syllabus - CBSE Exams 2021
Example 46 Important
Example 47 Important
Example 48 Important
Example 49
Example 50
Example 51 Important
About the Author