Question

Find a nonzero function f: R -> R such that (f o f)(r) = 0 for...

Find a nonzero function f: R -> R such that (f o f)(r) = 0 for all r E R. Does there exist such a function that is 1-1? Justify your answer.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Does there exist a continuous onto function f : [0, 1] → R? Does there exist...
Does there exist a continuous onto function f : [0, 1] → R? Does there exist a continuous onto function f : (0, 1) → (−1, 0) ∪ (0, 1)?
Consider the function f defined on R by f(x) = ?0 if x ≤ 0, f(x)...
Consider the function f defined on R by f(x) = ?0 if x ≤ 0, f(x) = e^(−1/x^2) if x > 0. Prove that f is indefinitely differentiable on R, and that f(n)(0) = 0 for all n ≥ 1. Conclude that f does not have a converging power series expansion En=0 to ∞[an*x^n] for x near the origin. [Note: This problem illustrates an enormous difference between the notions of real-differentiability and complex-differentiability.]
Let f : E → R be a differentiable function where E = [a,b] or E...
Let f : E → R be a differentiable function where E = [a,b] or E = (−∞,∞), show that if f′(x) not = 0 for all x ∈ E then f is one-to-one, i.e., there does not exist distinct points x1,x2 ∈ E such that f(x1) = f(x2). Deduce that f(x) = 0 for at most one x.
For the given function: f [0; 3]→R is continuous, and all of its values are rational...
For the given function: f [0; 3]→R is continuous, and all of its values are rational numbers. It is also known that f(0) = 1. Can you find f(3)?Justification b) Let [x] denote the smallest integer, not larger than x. For instance,[2.65] = 2 = [2], [−1.5] =−2. Caution: [x] is not equal to |x|! Find the points at which the function f : R→R. f(x) = cos([−x] + [x]) has or respectively, does not have a derivative.
Consider the function f : R 2 → R defined by f(x, y) = 4 +...
Consider the function f : R 2 → R defined by f(x, y) = 4 + x 3 + y 3 − 3xy. (a)Compute the directional derivative of f at the point (a, b) = ( 1 2 , 1 2 ), in the direction u = ( √ 1 2 , − √ 1 2 ). At the point ( 1 2 , 1 2 ), is u the direction of steepest ascent, steepest descent, or neither? Justify your...
[Series circuit analogue: RLC circuit with nonzero resistance R and nonzero voltage E(t) as forcing function...
[Series circuit analogue: RLC circuit with nonzero resistance R and nonzero voltage E(t) as forcing function is analogous to a forced damped spring/mass system.] Consider the RLC circuit with inductance L = 8 henrys, resistance R = 16 ohms, capacitance C = 0.025 farads, and voltage E(t) = 17 cos 2t volts. (a) Find the current in the circuit for t > 0, given that at time t = 0 the capacitor is uncharged and there is no current flowing....
Question 4: The function f : {0,1,2,...} → R is defined byf(0) = 7, f(n) =...
Question 4: The function f : {0,1,2,...} → R is defined byf(0) = 7, f(n) = 5·f(n−1)+12n2 −30n+15 ifn≥1.• Prove that for every integer n ≥ 0, f(n)=7·5n −3n2. Question 5: Consider the following recursive algorithm, which takes as input an integer n ≥ 1 that is a power of two: Algorithm Mystery(n): if n = 1 then return 1 else x = Mystery(n/2); return n + xendif • Determine the output of algorithm Mystery(n) as a function of n....
1. Find T5(x): Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0. T5(x)=   Using...
1. Find T5(x): Taylor polynomial of degree 5 of the function f(x)=cos(x) at a=0. T5(x)=   Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.00054 of the right answer. Assume for simplicity that we limit ourselves to |x|≤1. |x|≤ = 2. Use the appropriate substitutions to write down the first four nonzero terms of the Maclaurin series for the binomial:   (1+7x)^1/4 The first nonzero term is:     The second nonzero term is:     The third...
4. Let f be a function with domain R. Is each of the following claims true...
4. Let f be a function with domain R. Is each of the following claims true or false? If it is false, show it with a counterexample. If it is true, prove it directly from the FORMAL DEFINITION of a limit. (a) IF limx→∞ f(x) = ∞ THEN limx→∞ sin (f(x))  does not exist. (b) IF f(−1) = 0 and f(1) = 2 THEN limx→∞ f(sin(x)) does not exist.
i) F o r t h e f o l l o w I n g...
i) F o r t h e f o l l o w I n g f i n d t h e ( c o m p. E x p.) f o u r I e r s e r i e s f o r x( t ) I I ) D r a w t h e am p &. P h a s e s p e c t r a I I I ) T...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT