BBS1014 & MB104 Functions Tutorial 3 PDF
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Uploaded by KnowledgeableCantor
UCSI University
Prof. Ts. Dr. Ganeshsree
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Summary
This document provides a tutorial on functions, including composition, inverses, and determining if functions are odd, even or neither odd nor even. The tutorial has various questions on these topics. It's a valuable resource for students studying calculus and analytical geometry.
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BBS1014 CALCULUS AND ANALYTICAL GEOMETRY MB104 CALCULUS AND ANALYTICAL GEOMETRY FOR APPLIED SCIENCES TOPIC 1 : FUNCTIONS TUTORIAL 3 Answer ALL questions and show ALL working. Clearly label and present your work in a cl...
BBS1014 CALCULUS AND ANALYTICAL GEOMETRY MB104 CALCULUS AND ANALYTICAL GEOMETRY FOR APPLIED SCIENCES TOPIC 1 : FUNCTIONS TUTORIAL 3 Answer ALL questions and show ALL working. Clearly label and present your work in a clean and coherent format. State any assumptions made and conclusions drawn clearly. Question 1 For the functions given below, find the following: (a) 𝑓(𝑥) = 𝑥 3 + 2𝑥 2 , 𝑔(𝑥) = 3𝑥 2 − 1 (i) 𝑓+𝑔 (ii) 𝑓−𝑔 (iii) 𝑓 ∘ 𝑔 (iv) 𝑔∘𝑓 1 (b) 𝑓(𝑥) = 𝑥 , 𝑔(𝑥) = 𝑥 3 + 2𝑥 (i) 𝑓+𝑔 (ii) 𝑓−𝑔 (iii) 𝑓∘𝑔 (iv) 𝑔∘𝑓 Question 2 Find the composition of the following functions: (a) Let 𝑓(𝑥) = 𝑥 2 + 2𝑥, 𝑔(𝑥) = 𝑥 − 1. Then find: (i) 𝑓∘𝑔 (ii) 𝑔∘𝑓 1 (b) Let 𝑓(𝑥) = 𝑥 + 4, 𝑔(𝑥) = 2 − 11𝑥, ℎ(𝑥) = 𝑥. Then find: (i) 𝑓∘𝑔∘ℎ (ii) 𝑔∘𝑓∘ℎ (iii) ℎ∘𝑓∘𝑔 Prof. Ts. Dr. Ganeshsree/BBS1014&MB104_Calculus and Analytical Geometry/Topic 1_Functions Page 1 Question 3 Determine the inverse functions of the following functions: 1 (a) 𝑓(𝑥) = 5 (4𝑥 − 3) 𝑥+2 (b) 𝑓(𝑥) = 𝑥+1 , 𝑥 ≠ −1 9 (c) 𝑓(𝑥) = 5 𝑥 + 32 (d) 𝑓(𝑥) = 𝑥 2 − 1, 𝑥 ≥ 0 (e) 𝑓(𝑥) = 𝑥 + 1 (f) 𝑓(𝑥) = √𝑥 + 1 1 (g) 𝑓(𝑥) = − 𝑥−3 (h) 𝑓(𝑥) = (𝑥 − 3)2 , 𝑥 ≥ 3 Question 4 Determine whether the following functions are odd, even or neither odd nor even. (a) 𝑓(𝑥) = 3𝑥 − √2 (b) 𝑔(𝑥) = 3𝑥 2 + 2𝑥 − 1 𝑥3 (c) 𝑔(𝑥) = 8 (d) 𝑓(𝑥) = 𝑥 + 𝑥 3 2 (e) 𝑓(𝑥) = 2𝑥 2 + 𝑥 − 4 Prof. Ts. Dr. Ganeshsree/BBS1014&MB104_Calculus and Analytical Geometry/Topic 1_Functions Page 2
