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Question 9. Consider the real functions: r2 - 4 f(x) :- х — 2 g(x) = x + 2. Are these functions equal?

Question 9. Consider the real functions: r2 - 4 f(x) :- х — 2 g(x) = x + 2. Are these functions equal?

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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Please help me with question 9 

Question 8. What is the domain of f(x) = v3 – x? Because functions are also sets of ordered pairs (like relations), we can say that f and g are equal if and only if f Cg and g C f. Definition 4. Two functions f : A → B and g : A → D are equal if f g (as sets). Notice also that the domains of two equal functions must be the same. We characterize equality in an equivalent manner below: Theorem 1. Two functions f and g are equal if and only if 1. Dom(f) Dom(g) and 2. for all x E Dom(f), f(x) = g(x) Question 9. Consider the real functions: x² – 4 f(x) = g(x) = x + 2. х — 2 Are these functions equal?
Transcribed Image Text:Question 8. What is the domain of f(x) = v3 – x? Because functions are also sets of ordered pairs (like relations), we can say that f and g are equal if and only if f Cg and g C f. Definition 4. Two functions f : A → B and g : A → D are equal if f g (as sets). Notice also that the domains of two equal functions must be the same. We characterize equality in an equivalent manner below: Theorem 1. Two functions f and g are equal if and only if 1. Dom(f) Dom(g) and 2. for all x E Dom(f), f(x) = g(x) Question 9. Consider the real functions: x² – 4 f(x) = g(x) = x + 2. х — 2 Are these functions equal?
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