Ex 1.3 , 4
Last updated at May 29, 2018 by Teachoo
Last updated at May 29, 2018 by Teachoo
Transcript
Ex1.3 , 4 If 𝑓(𝑥)=(4𝑥 − 3)6𝑥 − 4, 𝑥 ≠ 23 , show that 𝑓𝑜𝑓(𝑥)=𝑥, for all 𝑥 ≠ 23 . What is the inverse of f? 𝑓(𝑥)=(4𝑥 − 3)6𝑥 − 4 𝑓(𝑓𝑥) = 4𝑓(𝑥) − 36𝑓(𝑥) − 4 𝑓𝑜𝑓𝑥 = 44𝑥 − 36𝑥 − 4 − 364𝑥 − 36𝑥 − 4 − 4 = 44𝑥 − 3 − 36𝑥 − 46𝑥 − 464𝑥 − 3 − 46𝑥 − 46𝑥 − 4 = 16𝑥 − 12 − 18𝑥 +126𝑥 − 424𝑥 − 18 − 24𝑥 +166𝑥 − 4 = 16𝑥 − 12 − 18𝑥 +126𝑥 − 4 × 6𝑥 − 424𝑥 − 18 − 24𝑥 + 16 = 16𝑥 − 12 − 18𝑥 +1224𝑥 −18 −24𝑥 +16 = −2𝑥 + 00 − 2 = −2𝑥− 2 = x ∴ 𝑓𝑜𝑓𝑥 = x Calculating inverse of f(x) 𝑓(𝑥)=(4𝑥 − 3)6𝑥 − 4 Put f(x) = y y = (4𝑥 − 3)6𝑥 − 4 y(6x – 4) = (4x – 3) 6xy – 4y = 4x – 3 6xy – 4x = 4y – 3 x(6y – 4) = 4y – 3 x = 4𝑦 − 36𝑦 − 4 So, inverse of f = 4𝑦 − 36𝑦 − 4 ∴ Let inverse of f = g (y) = 4𝑦 − 36𝑦 − 4 g (y) = 4𝑦 − 36𝑦 − 4 Replacing y with x g (x) = 4𝑥 − 36𝑥 − 4 = f(x) Hence we can say inverse of f is f itself i.e. f -1 = f
Finding Inverse
Inverse of a function
How to check if function has inverse?
Example 22 Deleted for CBSE Board 2022 Exams
Ex 1.3, 5 (i) Deleted for CBSE Board 2022 Exams
How to find Inverse?
Example 28 (a) Deleted for CBSE Board 2022 Exams
Misc 11 (i) Important Deleted for CBSE Board 2022 Exams
Ex 1.3, 11 Deleted for CBSE Board 2022 Exams
Example 27 Important Deleted for CBSE Board 2022 Exams
Misc 1 Deleted for CBSE Board 2022 Exams
Ex 1.3 , 6 Deleted for CBSE Board 2022 Exams
Ex 1.3, 14 (MCQ) Important Deleted for CBSE Board 2022 Exams
Example 23 Important Deleted for CBSE Board 2022 Exams
Misc 2 Deleted for CBSE Board 2022 Exams
Ex 1.3 , 4 Deleted for CBSE Board 2022 Exams You are here
Example 24 Deleted for CBSE Board 2022 Exams
Ex 1.3 , 8 Important Deleted for CBSE Board 2022 Exams
Example 25 Important Deleted for CBSE Board 2022 Exams
Ex 1.3 , 9 Important Deleted for CBSE Board 2022 Exams
Finding Inverse
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