![1. [2] Is the function f :Q\ {0} →Q defined by f(x) = 1 + 2 onto? Why or why not? 2. [3] Let A = {1, 2, 3, 4, 5,6}, and f: A+](http://img.homeworklib.com/questions/698877e0-9177-11eb-a794-7f77167a7484.png?x-oss-process=image/resize,w_560)
Homework Answers
- Let f be the function from R to R defined by f(x)=x2.Find a) f−1({1}). b)...
- Let f be the function from R to R defined by f(x)=x2.Find a) f−1({1}). b) f−1({x | 0 < x < 1} c) f−1({x|x>c) f−1({x|x>4}). -Show that the function f (x) = e x from the set of real numbers to the set of real numbers is not invertible but if the codomain is restricted to the set of positive real numbers, the resulting function is invertible.
QUESTION 16 Let X={1,2,3,4} and T={0,X,{1,2}, {3,4}}. Let f: (X,T) → (X,T) defined by f(1) =...
QUESTION 16 Let X={1,2,3,4} and T={0,X,{1,2}, {3,4}}. Let f: (X,T) → (X,T) defined by f(1) = 3 , f(2)= 1, f(3) = 4 ,f(4) = 2. Then f is continuous at 2. True False QUESTION 12 The function f(x) = xis open. True False QUESTION 6 Let f: X→ Y be a continuous function and A be a path connected in X, then f(A) is connected in Y. True False
let f:[-pi,pi] -> R be definded by the function f(x) { -2 if -pi<x<0 2 if...
let f:[-pi,pi] -> R be definded by the function f(x) { -2
if -pi<x<0 2 if 0<x<pi
a) find the fourier series of f and describe its convergence
to f
b) explain why you can integrate the fourier series of f term
by term to obtain a series representation of F(x) =|2x| for x in
[-pi,pi] and give the series representation
DO - - - 1. Let f: [-T, 1] + R be defined by the function S-2 if-A53 <0...
5. Let be the function defined by f(x) = -1 3 1.5 if r <0 if...
5. Let be the function defined by f(x) = -1 3 1.5 if r <0 if 0<x<2 if 3 < r <5 Find the Lebesgue integral of f over (-10,10).
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a functi...
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a function of the form q (x) = kxm (4) (b) Approximate f with a function of the form g2(x) = be Which approximation between q and g2 1s more appropriate for the given data? Justify your (3) (c) answer < In, and a piecewise cubic polynomial Consider a set of points (I,) Such that...
Define four sets of integers Let P {0, 1), let Q {-11, 1, 5) , and...
Define four sets of integers Let P {0, 1), let Q {-11, 1, 5) , and Let R and S be arbitrary nonempty subsets of Z. Define an even indicator function F F: ZP by F(x) = (x + 1) mod 2 for x e Z That is, F(x) 1 if x is even, and F(x) = 0 if x is odd. or neither? Explain. a) Is F: Q P one-to-one, onto, both, or neither? Explain. b) Is F: (Pn...
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on th...
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
Let f be the function defined by F(x)=(1/2)(x+2)^2 for [-2,0) and 2-2sin(sqrtx) for [0, (x^3)/4]. the...
Let
f be the function defined by F(x)=(1/2)(x+2)^2 for [-2,0) and
2-2sin(sqrtx) for [0, (x^3)/4]. the graph of f is shown in the
figure above. Let R be the regiok bounded by the graph of f and the
x-axis.
for -25=co for osca Let I be the function defined by 1 (2) - {}(2+2) (2-2n The graph of fis shown in the figure above. Let R be the region bounded by the graph off and the ads (a) Find the...
Let f : [0,∞) → R be the function defined by f ( x ) =...
Let f : [0,∞) → R be the function defined by
f ( x ) = 2 ⌊ x ⌋ − x?
where x? = x − ⌊x⌋ is the decimal part of x. Prove that f is
injective.
Let f: 0,00) + R be the function defined by f(3) = 212) where ã = x — [x] is the decimal part of x. Prove that f is injective.
Ty f) -1 0 2 The above diagram is a plot of a function f(x) Is f(x) continuous at 0 and why? Choo...
ty f) -1 0 2 The above diagram is a plot of a function f(x) Is f(x) continuous at 0 and why? Choose the best response below: Yes, the function is continous at x=0, as it has a two-sided limit as x approaches 0, which is equal to f(0) itself No, because the function does not have a two-sided limit as x approaches 0 No, because the function is not defined at x0. No, because the limit of the function...
QUESTION 16 Let X={1,2,3,4} and T={0,X,{1,2}, {3,4}}. Let f: (X,T) → (X,T) defined by f(1) = 3 , f(2)= 1, f(3) = 4 ,f(4) = 2. Then f is continuous at 2. True False QUESTION 12 The function f(x) = xis open. True False QUESTION 6 Let f: X→ Y be a continuous function and A be a path connected in X, then f(A) is connected in Y. True False
let f:[-pi,pi] -> R be definded by the function f(x) { -2
if -pi<x<0 2 if 0<x<pi
a) find the fourier series of f and describe its convergence
to f
b) explain why you can integrate the fourier series of f term
by term to obtain a series representation of F(x) =|2x| for x in
[-pi,pi] and give the series representation
DO - - - 1. Let f: [-T, 1] + R be defined by the function S-2 if-A53 <0...
5. Let be the function defined by f(x) = -1 3 1.5 if r <0 if 0<x<2 if 3 < r <5 Find the Lebesgue integral of f over (-10,10).
(3.2) Consider the data given in the following table 05 1 15 f(x) 0 2 0 6 1 2 20 (4) (a) Approximate f with a function of the form q (x) = kxm (4) (b) Approximate f with a function of the form g2(x) = be Which approximation between q and g2 1s more appropriate for the given data? Justify your (3) (c) answer < In, and a piecewise cubic polynomial Consider a set of points (I,) Such that...
Define four sets of integers Let P {0, 1), let Q {-11, 1, 5) , and Let R and S be arbitrary nonempty subsets of Z. Define an even indicator function F F: ZP by F(x) = (x + 1) mod 2 for x e Z That is, F(x) 1 if x is even, and F(x) = 0 if x is odd. or neither? Explain. a) Is F: Q P one-to-one, onto, both, or neither? Explain. b) Is F: (Pn...
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
Let
f be the function defined by F(x)=(1/2)(x+2)^2 for [-2,0) and
2-2sin(sqrtx) for [0, (x^3)/4]. the graph of f is shown in the
figure above. Let R be the regiok bounded by the graph of f and the
x-axis.
for -25=co for osca Let I be the function defined by 1 (2) - {}(2+2) (2-2n The graph of fis shown in the figure above. Let R be the region bounded by the graph off and the ads (a) Find the...
Let f : [0,∞) → R be the function defined by
f ( x ) = 2 ⌊ x ⌋ − x?
where x? = x − ⌊x⌋ is the decimal part of x. Prove that f is
injective.
Let f: 0,00) + R be the function defined by f(3) = 212) where ã = x — [x] is the decimal part of x. Prove that f is injective.
ty f) -1 0 2 The above diagram is a plot of a function f(x) Is f(x) continuous at 0 and why? Choose the best response below: Yes, the function is continous at x=0, as it has a two-sided limit as x approaches 0, which is equal to f(0) itself No, because the function does not have a two-sided limit as x approaches 0 No, because the function is not defined at x0. No, because the limit of the function...
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