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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ec07f59-db17-4869-86ed-f1dcc59bb208%2F1e50b1e5-4abc-4014-b451-626a21bd1c7b%2Flf81o0a_processed.jpeg&w=3840&q=75)
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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