Given f:R R, let O(f) be the set of all functions g for which there...

 

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Given f:R → R, let O(f) be the set of all functions g for which there exist positive constants c, a e Rsuch that Ig(x)| < c[f(x)| for all x > a. a. (4 pts) Write the negation of the statement "g e O(f)" in symbols using quantifiers; then write it out in words and give a brief explanation of its meaning. b. (2 pts) Let f be the constant functionf = 1. If g(x) = (5x 4+4) / (x*+1), is it true that ge O(f)? Justify your answer. c. (2 pts) Let f(x) = x and g(x) = x2. Is it true that g e O(f)? Justify your answer. Given f:R → R, let O(f) be the set of all functions g for which there exist positive constants c, a e Rsuch that Ig(x)| < c[f(x)| for all x > a. a. (4 pts) Write the negation of the statement "g e O(f)" in symbols using quantifiers; then write it out in words and give a brief explanation of its meaning. b. (2 pts) Let f be the constant functionf = 1. If g(x) = (5x 4+4) / (x*+1), is it true that ge O(f)? Justify your answer. c. (2 pts) Let f(x) = x and g(x) = x2. Is it true that g e O(f)? Justify your answer.

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