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Ex 1.3

Ex 1.3, 1
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Ex 1.3, 2 Deleted for CBSE Board 2023 Exams

Ex 1.3, 3 (i) Important Deleted for CBSE Board 2023 Exams

Ex 1.3, 3 (ii) Deleted for CBSE Board 2023 Exams

Ex 1.3 , 4 Deleted for CBSE Board 2023 Exams

Ex 1.3, 5 (i) Deleted for CBSE Board 2023 Exams

Ex 1.3, 5 (ii) Important Deleted for CBSE Board 2023 Exams

Ex 1.3, 5 (iii) Important Deleted for CBSE Board 2023 Exams

Ex 1.3 , 6 Deleted for CBSE Board 2023 Exams

Ex 1.3 , 7 Deleted for CBSE Board 2023 Exams You are here

Ex 1.3 , 8 Important Deleted for CBSE Board 2023 Exams

Ex 1.3 , 9 Important Deleted for CBSE Board 2023 Exams

Ex 1.3, 10 Important Deleted for CBSE Board 2023 Exams

Ex 1.3, 11 Deleted for CBSE Board 2023 Exams

Ex 1.3, 12 Deleted for CBSE Board 2023 Exams

Ex 1.3, 13 (MCQ) Important Deleted for CBSE Board 2023 Exams

Ex 1.3, 14 (MCQ) Important Deleted for CBSE Board 2023 Exams

Chapter 1 Class 12 Relation and Functions

Serial order wise

Last updated at May 29, 2018 by Teachoo

Ex 1.3 , 7 (Method 1) Consider f: R R given by f(x) = 4x+ 3. Show that f is invertible. Find the inverse of f. Checking inverse Step 1 f(x) = 4x + 3 Let f(x) = y y = 4x + 3 y 3 = 4x 4x = y 3 x = 3 4 Let g(y) = 3 4 where g: R R Step 2: gof = g(f(x)) = g(4x + 3) = (4 + 3) 3 4 = 4 + 3 3 4 = 4 4 = x = IR Step 3: fog = f(g(y)) = f 3 4 = 4 3 4 + 3 = y 3 + 3 = y + 0 = y = IR Since gof = IR and fog = IR, f is invertible & Inverse of f = g(y) = Ex 1.3 , 7 (Method 2) Consider f: R R given by f(x) = 4x+ 3. Show that f is invertible. Find the inverse of f. f is invertible if f is one-one and onto Checking one-one f(x1) = 4x1 + 3 f(x2) = 4x2 + 3 Putting f(x1) = f(x2) 4x1 + 3 = 4x2 + 3 4x1 = 4x2 x1 = x2 If f(x1) = f(x2) , then x1 = x2 f is one-one Checking onto f(x) = 4x + 3 Let f(x) = y, where y Y y = 4x + 3 y 3 = 4x 4x = y 3 x = 3 4 Here, y is a real number So, 3 4 is also a real number So, x is a real number Thus, f is onto Since f is one-one and onto f is invertible Finding inverse f(x) = 4x + 3 For finding inverse, we put f(x) = y and find x in terms of y We have done that while proving onto y = f(x) y = 4x + 3 x = 3 4 Let g(y) = 3 4 where g: R R Inverse of f = g(y) =