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1. Let f: R → R be defined by f(x) = 2x – 3. Now f is one-to-one and onto; hence f has an inverse function f-1. Find a formula for f-1. 2. Determine whether the following functions are injective, surjective or bijective. For any bijections write down the inverse. i. f:R → R given by f(x) = x² + x + 1. ii. f:N → N given by f (x) = x² +x + 1.

1. Let f: R → R be defined by f(x) = 2x – 3. Now f is one-to-one and onto; hence f has an inverse function f-1. Find a formula for f-1. 2. Determine whether the following functions are injective, surjective or bijective. For any bijections write down the inverse. i. f:R → R given by f(x) = x² + x + 1. ii. f:N → N given by f (x) = x² +x + 1.

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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1. Let f: R → R be defined by f(x) = 2x – 3. Now f is one-to-one and onto; hence f has an inverse function f-1. Find a formula for f-1. 2. Determine whether the following functions are injective, surjective or bijective. For any bijections write down the inverse. i. f:R → R given by f(x) = x² + x + 1. ii. f:N → N given by f (x) = x² +x + 1.
Transcribed Image Text:1. Let f: R → R be defined by f(x) = 2x – 3. Now f is one-to-one and onto; hence f has an inverse function f-1. Find a formula for f-1. 2. Determine whether the following functions are injective, surjective or bijective. For any bijections write down the inverse. i. f:R → R given by f(x) = x² + x + 1. ii. f:N → N given by f (x) = x² +x + 1.
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