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(c) Determine with justification whether each of the following functions R → R is one-to-one, onto or bijective. i. fi(x) = 2x + 5 ii. f2(x) = x² + 2x +1 iii. f3(x) = exp¯²

(c) Determine with justification whether each of the following functions R → R is one-to-one, onto or bijective. i. fi(x) = 2x + 5 ii. f2(x) = x² + 2x +1 iii. f3(x) = exp¯²

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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Question 3 (a) Minimise the following logic function using the Karnaugh maps method: f(x, y, z) = x'y'2' + x'y + xyz' + xz (b) Given the following logical circuit with three inputs A, B and C: output i. Use the boolean algebra notation and write down the boolean expression of the output of this circuit. ii. Simplify the logical expression in (i). Explain your answer. (c) Determine with justification whether each of the following functions R → R is one-to-one, onto or bijective. i. fi(x) = 2x + 5 ii. f2(x) = x² + 2x + 1 iii. f3(x) = exp¯ (d) Prove by induction that 5 "-1 is divisible by 5 for all n e Z +.
Transcribed Image Text:Question 3 (a) Minimise the following logic function using the Karnaugh maps method: f(x, y, z) = x'y'2' + x'y + xyz' + xz (b) Given the following logical circuit with three inputs A, B and C: output i. Use the boolean algebra notation and write down the boolean expression of the output of this circuit. ii. Simplify the logical expression in (i). Explain your answer. (c) Determine with justification whether each of the following functions R → R is one-to-one, onto or bijective. i. fi(x) = 2x + 5 ii. f2(x) = x² + 2x + 1 iii. f3(x) = exp¯ (d) Prove by induction that 5 "-1 is divisible by 5 for all n e Z +.
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