5. (a) Let f: R R be defined by f(x) = x², let g: RR be defined by g(x) = sin x, and let h: R→ R be defined by h(x) = 3√x. Determine formulas for [(hog) of] (x) and [ho (go f)](x). Does this prove that (hog) of = ho (go f) for these particular functions? Explain. (b) Now let A, B, C, and D be sets and let f: A → B, g: B → C, and h: CD. Prove that (hog) of = ho (go f). That is, prove that function composition is an associative operation. BY NC SA
5. (a) Let f: R R be defined by f(x) = x², let g: RR be defined by g(x) = sin x, and let h: R→ R be defined by h(x) = 3√x. Determine formulas for [(hog) of] (x) and [ho (go f)](x). Does this prove that (hog) of = ho (go f) for these particular functions? Explain. (b) Now let A, B, C, and D be sets and let f: A → B, g: B → C, and h: CD. Prove that (hog) of = ho (go f). That is, prove that function composition is an associative operation. BY NC SA
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![5. (a) Let f: R R be defined by f(x) = x², let g: RR be defined by
g(x) = sin x, and let h: R→ R be defined by h(x) = 3√x.
Determine formulas for [(hog) of] (x) and [ho (go f)](x).
Does this prove that (hog) of = ho (go f) for these particular
functions? Explain.
(b) Now let A, B, C, and D be sets and let f: A → B, g: B → C, and
h: CD. Prove that (hog) of = ho (go f). That is, prove that
function composition is an associative operation.
BY NC SA](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fed04f254-2b14-4f51-a897-ea8ba8024a7a%2F9a03925e-0ce0-4f0a-a05f-e56809b689b6%2Fs489gnb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. (a) Let f: R R be defined by f(x) = x², let g: RR be defined by
g(x) = sin x, and let h: R→ R be defined by h(x) = 3√x.
Determine formulas for [(hog) of] (x) and [ho (go f)](x).
Does this prove that (hog) of = ho (go f) for these particular
functions? Explain.
(b) Now let A, B, C, and D be sets and let f: A → B, g: B → C, and
h: CD. Prove that (hog) of = ho (go f). That is, prove that
function composition is an associative operation.
BY NC SA
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