RQ12 - Composite Functions and Inverse Functions.pdf -...

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C OMPOSITE F UNCTIONS AND I NVERSE F UNCTIONS All questions are taken from Stitz & Zeager, 2013. Q1 6 Use the given pair of functions to find and simplify expressions for the following functions and state the domain of each using interval notation. (? ∘ ?)(?) (? ∘ ?)(?) (? ∘ ?)(?) 1. ?(?) = ? 2 − ? + 1, ?(?) = 3? − 5 2. ?(?) = 3? − 5, ?(?) = √? 3. ?(?) = 3 − ? 2 , ?(?) = √? + 1 4. ?(?) = ? 2 − ? − 1, ?(?) = √? − 5 5. ?(?) = 3? ? − 1 , ?(?) = ? ? − 3 6. ?(?) = 2? ? 2 − 4 , ?(?) = √1 − ? Q7 12 Let ? be the function defined by and let ? be the function be defined Find the value if it exists. 7. ?(?(−1)) 8. (? ∘ ?)(−3) 9. ?(?(−3)) 10. (? ∘ ?)(−2) 11. ? (?(?(−1))) 12. (? ∘ ? ∘ … ∘ ?)(0) Q13 18 Use the graphs of ? = ?(?) and ? = ?(?) below to find the function value. 13. (? ∘ ?)(1) 14. (? ∘ ?)(3) 15. (? ∘ ?)(2) 16. (? ∘ ?)(0) 17. (? ∘ ?)(1) 18. (? ∘ ?)(1)
19. 20. Q21 28 Find the inverse of the functions below. 21. ?(?) = √3? − 1 + 5 22. ?(?) = 3√? − 1 − 4 23. ?(?) = √3? − 1

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