Need detailed solutions, wrong will be downvoted, no AI. i know the correct answer If f : R → R is a function defined by f(x) = [x − 1] cos (2221) π, where [.] denotes the greatestinteger function, then f is:(1) discontinuous only at x = 1(2) discontinuous at all integral values of x except at x = 1(3) continuous only at x =1(4) continuous for every real x

Answered: Image /qna-images/answer/c1bca858-1a09-4099-a704-f879e8fd017a.jpg

Answered: If f : R → R is a function defined by…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.5: The Kernel And Range Of A Linear Transformation

Problem 30EQ

See similar textbooks

Similar questions

5. Prove that the equation has no solution in an ordered integral domain.
Find all differentiable functions f: R→R such that f'(x) = F(x + n) – f(x) n for all real numbers x and all positive integers n.
Let f(x) = x. Show directly that f ∊ R[0, 2]
Let f : R → R be a twice differentiable function such that f" + f = 0. Prove there exist constants cl and c2 such that, for all real x, f(x) = c1sinx + c2cosx. We are assuming here that we know all the basic properties of sines and cosines, such as (sinx)' =cosx. (Hint: what can you say about the functions f(x)cosx – f'(x)sinx and f(x)sinx + f'(x)cos 2?)
Show that the following relation is not a function on R {(x, y) ∈ R × R : x = cos(y)},
Consider the function f: RR defined by f(x) = 0 if x is irrational and f(x) = 1 if x is rational Is f integrable over [0, 1] (or any other bounded and closed interval)?
Let S(x²+2x)², x>1, lax+bx², f(x) = x<1. Compute for all a and b such that the function f(x) is differentiable.
Let n be a positive integer. Define the function fn (2) by dzn (2² Find the value of f(-1 + i). fn(z) = + 2x + 2)".
Let f(x)=x²-2x on [-5, 1]. Use the IVT to determine if there is a solution to f(x) = 15 in the interval between -5 and 1. If so, find the value of c in the interval such that f(c) = 15. O O O f(x) is continuous on [-5, 1] 15 is between f(-5) = 35 and f(1) = -1 C = -3 f(x) is continuous on [-5, 1] 15 is between f(-5) = 35 and f(1) = -1 c=5 f(x) is continuous on [-5, 1] 15 is between f(-5) = 35 and f(1) = -1 c = -3, c=5
Show that the function f:R to R defined by f(x)=5x-12 is continuous using the E-d definition.
(d) Prove that the function fcx) = x is Continous but not unifomly Continous on the imntenal X=(0,00) ap nte %3D X69 ततीनाहिने
Let D²[a, b] = set of all twice differentiable functions on the interval [a, b] with a continuous second derivative. For example, f(x) = sin r is a member of D2 [a, b] because it is a twice differentiable function with f"(x) = - sin z and the second derivative f"(x) = - sin r is a continuous function. It can be shown that D²[a, b] is a vector space (you can take it for granted for this question) with the same operations we defined on F([a, b]) in the class. Note: Like in F([a, b]), the zero element of D²[a,b] is ƒ(x) = 0 for every x in [a, b], i.e., 0(x) = 0 for every a in [a, b]. (a) If W = {f € D²[0, 1]|f"(x) + 2f' (x) = f(0) + f(1) for very x E [0, 1]}}, show that W is a subspace of D²[0, 1]. (b) Let W = {f e D²[0, 1]| So' f²(x) + f(x)dxr = 0}. Is W a subspace of D²[0, 1]? %3D

SEE MORE QUESTIONS

Recommended textbooks for you

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Linear Algebra: A Modern Introduction

Algebra

ISBN:

9781285463247

Author:

David Poole

Publisher:

Cengage Learning

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

SEE MORE TEXTBOOKS

If f : R → R is a function defined by f(x) = [x − 1] cos (2221) π, where [.] denotes the greatest integer function, then f is: (1) discontinuous only at x = 1 (2) discontinuous at all integral values of x except at x = 1 (3) continuous only at x = 1 (4) continuous for every real x