help me. 5. consider set F(R):ff: f:R-R), but set all function with set real number in...
question3 3. * Let f be an entire function which restricts to a real function f:R R on the real axis. Show that for all z e C, f(z) = f(z). (Hint: refer to Problem set 2 Qn 1.)
(2) Consider the function f given by f:R R f(a)1 2 (a) Determine the domain D and range R of the function f. (b) Show that f is not one to one on D. (c) Let ç D be a subset of the domain of f such that for all x ? S, 0 and the function is one to one. Find such a set S. (d) For the set S given in Part (c), find f (x) (e) Determine...
5. [2 pts] Consider a function f: Z → Z and f(x) = x'. Answer the following questions. a. Is f(x) invertible? Justify your answer. b. Suppose that the domain and codomain change to real number, thus f:R → R. Then is f(x) invertible? Justify your answer.
1. Let f:R → R be the function defined as: 32 0 if x is rational if x is irrational Prove that lim -70 f(x) = 0. Prove that limc f(x) does not exist for every real number c + 0. 2. Let f:R + R be a continuous function such that f(0) = 0 and f(2) = 0. Prove that there exists a real number c such that f(c+1) = f(c). 3 Let f. (a,b) R be a function...
Is x = 0 a relative extrema for function f : R → R that is given by f(x) = sinx − cosx − 1/2(1 + x)^2 Question 3. Is x = 0 a relative extrema for function f:R + R that is given by 1 COS X f(x) = sin x (1 + x)? 2 Prove your claim. State any theorem that is applied in your proof.
Let R represent the set of all real numbers. Suppose f:R -> R has the rule f(x)=3x+2. Determine whether f is injective, surjective and/or bijective. Injective but not Surjective Surjective but not Injective Bijective (both Injective and Surjective) None of the above
show all steps please 5. Functions f:R R: 9: R R are both one to one on the set of real numbers. Is the function f +9 also one to one? [Hint: Be creative! Make up two one to one functions.
- 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.
3. Let the function f be a real valued bounded continuous function on R. Prove that there is a solution of the equation f(x) = x, xER. Now choose a number a with f(a) > a and define the sequence (an) recursively by defining al = a and a叶1 = f(an), where n E N. If f is strictly increasing on R, show that (an) converges to a solution of the equation (0.1). This method for approximating the solution is...
(5) 20 pts) Let F= {f:R → R} - the set of all real-valued functions. Determine if the following statements are true or false. Explain why. (a) (5pt) VEF 39 EF fog=go f = id. (b) (5pt) 3f EF Vg E F fog=go f = id. (C) (5pt) V EF Vg E F fog=go f = id. (d) (5pt) 3f EF 39 EF fog=go f = id. Explain you answers. (e) (+5pt) Negate and simplify VEF 39 EF fog=go f...