




Get live Maths 1-on-1 Classs - Class 6 to 12
Ex 1.3
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
Last updated at March 16, 2023 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) =