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4. Determine which of the following are onto functions. (a) f:Z→Z; f(n)=n³ +1 (b) g:Q → Q; g(x)= n² (c) h:R → R; h(x)= x³ – x (d) k:R → R: k(x) = 5*

4. Determine which of the following are onto functions. (a) f:Z→Z; f(n)=n³ +1 (b) g:Q → Q; g(x)= n² (c) h:R → R; h(x)= x³ – x (d) k:R → R: k(x) = 5*

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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The question asks to determine which of the following functions are onto functions. (a) The function \( f: \mathbb{Z} \to \mathbb{Z} \) is defined by \( f(n) = n^3 + 1 \). (b) The function \( g: \mathbb{Q} \to \mathbb{Q} \) is defined by \( g(x) = n^2 \). (c) The function \( h: \mathbb{R} \to \mathbb{R} \) is defined by \( h(x) = x^3 - x \). (d) The function \( k: \mathbb{R} \to \mathbb{R} \) is defined by \( k(x) = 5^x \).
Transcribed Image Text:The question asks to determine which of the following functions are onto functions. (a) The function \( f: \mathbb{Z} \to \mathbb{Z} \) is defined by \( f(n) = n^3 + 1 \). (b) The function \( g: \mathbb{Q} \to \mathbb{Q} \) is defined by \( g(x) = n^2 \). (c) The function \( h: \mathbb{R} \to \mathbb{R} \) is defined by \( h(x) = x^3 - x \). (d) The function \( k: \mathbb{R} \to \mathbb{R} \) is defined by \( k(x) = 5^x \).
Expert Solution
Step 1

a) f:Z -->Z;

f(n) = n3 +1

There are numbers in the codomain, which has no preimage. so f is not onto.

 

b) g:Q --> Q;       g(x) = n2

g is not onto 

 

 

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