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You are given two functions, f:RR, f(x) = 3x and g:R→ R, g(x) = x + 1 a. Find and record the function created by the composition of f and g, denoted go f. b. Prove that your recorded function of step (a.) is both one-to-one and onto. That is prove, go f:RR; (gof)(x) = g(f(x)), is well-defined where indicates go f is a bijection. For full credit you must explicitly prove that go f is both one-to-one and onto, using the definitions of one-to-one and onto in your proof. Do not appeal to theorems. You must give your proof line-by-line, with each line a statement with its justification. You must show explicit, formal start and termination statements as shown in lecture examples. You can use the Canvas math editor or write your math statements in English. For example, the statement to be proved was written in the Canvas math editor. In English it would be: Prove that the composition of functions f and g is both one-to-one and onto.

You are given two functions, f:RR, f(x) = 3x and g:R→ R, g(x) = x + 1 a. Find and record the function created by the composition of f and g, denoted go f. b. Prove that your recorded function of step (a.) is both one-to-one and onto. That is prove, go f:RR; (gof)(x) = g(f(x)), is well-defined where indicates go f is a bijection. For full credit you must explicitly prove that go f is both one-to-one and onto, using the definitions of one-to-one and onto in your proof. Do not appeal to theorems. You must give your proof line-by-line, with each line a statement with its justification. You must show explicit, formal start and termination statements as shown in lecture examples. You can use the Canvas math editor or write your math statements in English. For example, the statement to be proved was written in the Canvas math editor. In English it would be: Prove that the composition of functions f and g is both one-to-one and onto.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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You are given two functions, f:R→ R, f(x) = 3r and g:R→ R, g(x) = x + 1 a. Find and record the function created by the composition of f and g, denoted go f. b. Prove that your recorded function of step (a.) is both one-to-one and onto. That is prove, go f:RR; (gof)(x) = g(f(x)), is well-defined where indicates go f is a bijection. For full credit you must explicitly prove that go f is both one-to-one and onto, using the definitions of one-to-one and onto in your proof. Do not appeal to theorems. You must give your proof line-by-line, with each line a statement with its justification. You must show explicit, formal start and termination statements as shown in lecture examples. You can use the Canvas math editor or write your math statements in English. For example, the statement to be proved was written in the Canvas math editor. In English it would be: Prove that the composition of functions f and g is both one-to-one and onto.
Transcribed Image Text:You are given two functions, f:R→ R, f(x) = 3r and g:R→ R, g(x) = x + 1 a. Find and record the function created by the composition of f and g, denoted go f. b. Prove that your recorded function of step (a.) is both one-to-one and onto. That is prove, go f:RR; (gof)(x) = g(f(x)), is well-defined where indicates go f is a bijection. For full credit you must explicitly prove that go f is both one-to-one and onto, using the definitions of one-to-one and onto in your proof. Do not appeal to theorems. You must give your proof line-by-line, with each line a statement with its justification. You must show explicit, formal start and termination statements as shown in lecture examples. You can use the Canvas math editor or write your math statements in English. For example, the statement to be proved was written in the Canvas math editor. In English it would be: Prove that the composition of functions f and g is both one-to-one and onto.
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