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CMPSC 360 Fall 2025 Homework 7
发布时间：2025-10-24
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CMPSC 360 Fall 2025
Homework 7
Question 1
Let f : R → R, g : R → R, and h : R — {—2} → R be defined as:
(a) Compute (h ∘ g ∘ f)(∞) and simplify.
(b) Find the domain of h ∘ g ∘ f.
(c) Find all real values of ∞ such that (h ∘ g ∘ f)(x) = 10/1.
Question 2
Prove that the function f : R — {—3} → R — {2} defined by 
is bijective. Then find its inverse function 
and verify that the domain of 
is R — {2}.
Question 3
Let the function f be defined by
(a) Determine the domain and range of f.
(b) Find the inverse function 
(x).
(c) Verify that f and f—1 are inverses of each other by showing that
Question 4
Suppose that 
represents the identity function on R, defined by (x) = x.
Given the functions:
find all real values of ∞ that satisfy
Question 5
Let h : 
→ be defined by h(x) = 2x and let i : → be defined by i(x) = √x. Determine the composition i 。h and find out if it is a bijection over the set of positive real numbers .
Question 6
Find a closed-form and recursive expression for the given sequences in part (a), (b) and (c). For part (d), mention yes/no if it is a sequence or not and write only a closed-form expression if it is a sequence:
(a) 3, −4, −11, −18, …
(b) 
(c) A sequence where each term is 7 less than the previous term, starting with the initial term −5.
(d) 2, −0.5, 2, −0.5, 2, …
Question 7
Use Σ notation and/or II notation to rewrite the following:
(a) 1 — 5 + 25 — 125 + … + ∞
(b) (2n — 1)(2n + 1)(2n + 3)(2n + 5) … (2n + 47)
(c) 
