Explain why the following statement must be True, or provide a counterexample to show that it can be False. If ?f and ?g are one-to-one functions defined on all of ℝR , then the function ℎ(?)=?(?)+?(?)h(x)=f(x)+g(x) is also one-to-one.
Explain why the following statement must be True, or provide a counterexample to show that it can be False. If ?f and ?g are one-to-one functions defined on all of ℝR , then the function ℎ(?)=?(?)+?(?)h(x)=f(x)+g(x) is also one-to-one.
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
Explain why the following statement must be True, or provide a counterexample to show that it can be False.
If ?f and ?g are one-to-one functions defined on all of ℝR , then the function ℎ(?)=?(?)+?(?)h(x)=f(x)+g(x) is also one-to-one.
Expert Solution
Step 1
Note: A function f from A to B is said to be one-to-one or injective if for all distinct elements in A has distinct image in B under f.
That is f(x) = f(y) implies x= y for all x, y belongs to A.
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