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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 1CR
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