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31. If f: R→ R and g: R → R are both onto, is f + g also onto? Justify your answer.

31. If f: R→ R and g: R → R are both onto, is f + g also onto? Justify your answer.

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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How do you solve #31?
27. b = 1, all positive real numbers b, x, and y with (-;-) logb = log x - log, y. 28. Prove that for all positive real numbers b, x, and y with b# 1, log, (xy) = log x +log, y. H 29. Prove that for all real numbers a, b, and x with b and x positive and b 1, log, (x) = a log, x. Exercises 30 and 31 use the following definition: If f: R→ R and g: R→ Rare functions, then the function (f+g): R → R is defined by the formula (f + g)(x) = f(x) + g(x) for all real numbers x. mob silni bonis 30. If f: R→ R and g: R→ R are both one-to-one, is f + g also one-to-one? Justify your answer. 33. T 31. If f: R → R and g: R → R are both onto, is f + g also onto? Justify your answer. Exercises 32 and 33 use the following definition: If f: R → R is a function and c is a nonzero real number, the function (c. f): R → R is defined by the formula (c. f)(x) = c. f(x) for all real numbers x. 32. Let f: R→ R be a function and c a nonzero real num- ber. If f is one-to-one, is c. f also one-to-one? Justify your answer. →R be a function and c a nonzero real number. , is c. f also onto? Justify your answer.
Transcribed Image Text:27. b = 1, all positive real numbers b, x, and y with (-;-) logb = log x - log, y. 28. Prove that for all positive real numbers b, x, and y with b# 1, log, (xy) = log x +log, y. H 29. Prove that for all real numbers a, b, and x with b and x positive and b 1, log, (x) = a log, x. Exercises 30 and 31 use the following definition: If f: R→ R and g: R→ Rare functions, then the function (f+g): R → R is defined by the formula (f + g)(x) = f(x) + g(x) for all real numbers x. mob silni bonis 30. If f: R→ R and g: R→ R are both one-to-one, is f + g also one-to-one? Justify your answer. 33. T 31. If f: R → R and g: R → R are both onto, is f + g also onto? Justify your answer. Exercises 32 and 33 use the following definition: If f: R → R is a function and c is a nonzero real number, the function (c. f): R → R is defined by the formula (c. f)(x) = c. f(x) for all real numbers x. 32. Let f: R→ R be a function and c a nonzero real num- ber. If f is one-to-one, is c. f also one-to-one? Justify your answer. →R be a function and c a nonzero real number. , is c. f also onto? Justify your answer.
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