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Problem 4. Consider the following functions. For each function: 1. draw the function diagram 2. determine if it is one-to-one, onto, and invertible. If a function is invertible, provide the inverse function. Justify each of your answers. 4(a) Let Az = {1,2,3}. Let f2: P(A2) → {0,1,2,3} be the function defined by f2(X) = |X|. Note that XSA2 4(b) Let f3: {ab}3 → {ab}3 defined by f3(S1s2s3) = S3S182. Note that the input is of the form s = S1s253, the 3 characters forming the string s.

Problem 4. Consider the following functions. For each function: 1. draw the function diagram 2. determine if it is one-to-one, onto, and invertible. If a function is invertible, provide the inverse function. Justify each of your answers. 4(a) Let Az = {1,2,3}. Let f2: P(A2) → {0,1,2,3} be the function defined by f2(X) = |X|. Note that XSA2 4(b) Let f3: {ab}3 → {ab}3 defined by f3(S1s2s3) = S3S182. Note that the input is of the form s = S1s253, the 3 characters forming the string s.

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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Problem 4. Consider the following functions. For each function: 1. draw the function diagram 2. determine if it is one-to-one, onto, and invertible. If a function is invertible, provide the inverse function. Justify each of your answers. 4(a) Let A2 = {1,2,3}. Let f2: P(A2) → {0,1,2,3} be the function defined by f2(X) = |X|. Note that XC A2 4(b) Let f3: {a,b}3→ {ab}³ defined by f3(S1s2s3) = S3S1S2. %D Note that the input is of the form s = s1s283, the 3 characters forming the string s.
Transcribed Image Text:Problem 4. Consider the following functions. For each function: 1. draw the function diagram 2. determine if it is one-to-one, onto, and invertible. If a function is invertible, provide the inverse function. Justify each of your answers. 4(a) Let A2 = {1,2,3}. Let f2: P(A2) → {0,1,2,3} be the function defined by f2(X) = |X|. Note that XC A2 4(b) Let f3: {a,b}3→ {ab}³ defined by f3(S1s2s3) = S3S1S2. %D Note that the input is of the form s = s1s283, the 3 characters forming the string s.
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