i'm not sure how to explain that c is injective and find the range of its inverse.
i'm not sure how to explain that c is injective and find the range of its...
Determine which of the following functions are injective, surjective, bijective (bijectivejust means both injective and surjective). And Find a left inverse for f or explain why none exists.Find a right inverse for f or explain why none exists. (a)f:Z−→Z, f(n) =n2. (d)f:R−→R, f(x) = 3x+ 1. (e)f:Z−→Z, f(x) = 3x+ 1. (g)f:Z−→Zdefined byf(x) = x^2 if x is even and (x −1)/2 if x is odd.
9. Explain why the function below is discontinuous at the given number a.Sketch the graph of the function 1 if x #-2 f(x)= х+2 a =-2 if 1 х%3D—2 9. Explain why the function below is discontinuous at the given number a.Sketch the graph of the function 1 if x #-2 f(x)= х+2 a =-2 if 1 х%3D—2
Question 12 of 23 (1 point) Find two functions f and g such that h(x)=(fog)(x) and f(x) * g() + x. n(x) = */7x +5 f(x)=0 and g(x)=0 Question 14 of 23 (1 point) The one-to-one function is given. Write an equation for the inverse function. 2 s(x) = х 3
6 (12) For each function in parts a through f, state a domain that, ifit was the domain of the given function, would make the function one-to-one, and explain your answer. If no such domain exists, explain why not. (Hint: graph the function and use the appropriate line test) a. f(x) x 2| b. g(x) 3D х? —1 с. q(х) 3D х2 - 3х — 4 d. k(x)x3 9 = е. f(x) %3D Зх — 1 f l(x) 2x +...
please show complete answers for a,b,c,d Find the solution to the given system that satisfies the given initial condition. -5 1 |x(t) 10 3 х'() 3 -3 1 (b) х(т) %—D (d) x(T/6) (с) x(- 2т)%3 (а) x(0) %3 -1 1 3 (а) x() 3D| | (Use parentheses to clearly denote the argument of each function.) Find the solution to the given system that satisfies the given initial condition. -5 1 |x(t) 10 3 х'() 3 -3 1 (b) х(т)...
(1) For each of the following functions, determine if it is injective and determine if it is surjective. Justify your answer. (a) f : R → R, f(x) = 2x + 3. (b) g : R → R 2 , g(x) = (2x, 3x −1). (c) h : R 2 → R, h((x, y)) = x + y + 1. (d) j : {1, 2, 3} → {4, 5, 6}, j(1) = 5, j(2) = 4, j(3) = 6. (2)...
Can someone please check to see if I am doing this right? Please write legibly if you post revisions in comments, thank you! (5) Let A {q, r, s, t and B = {17, 18, 19, 20}. Determine which of the following are functions. Explain why or why not. а. fSAX В, where f — 1. q, 17), (r, 18), (s, 19), (s, 20) Answer: this is a function because in function 'f element 's' is related to 1 element...
1. (6 marks) Provide the domain, target, and range of the following functions (a, b, c, d}3 . For each x E(a, b, cF, fx)-dx. a) fta, b. c}2 b) g: {a, b, c, d)-(a, b, c, d}?. For each x E(a, b, c, d], g(x) (4 marks) Use the ceiling and floor functions to qive a mathematical expression for the following a) Among a random group of 100 people at least 9 must be born in the same month...
can please explain why F(sigma)= u? We consider the PDE: for given o(t) € H|(12) find the (weak) solution u € H}(2) of V. (g(x)Vu(x)) = 1. The corresponding parameter-to-solution map is defined as F: D(F):= H (1) C H²(2) L’(1) F(o)= u uc H (12) c L’(2) solving b(u, w;o) = f(w) for all w e H7(), b(u, w; 0) := ( D2.Vwdi, f(w):=- / w dr. The associated inverse problem is for u E L(12) find o E...
Explain relationships and properties between inverse functions 1. Consider how Alex, Jordan and Kelly found the inverse function of f(x) = Alex's work Jordan's work y = ²X+1 foftly) f(x)= y x + 1 ore So: x=2/34 +1 x-1= 234 V - y I f(f="(y)) = 2 / 3 f (y) + 1 = y 2/3f-lly)=4-1 (y) (y) Kelly's work 6 y = 2x + 1 9-1= 2x 3(4-1) = 2x 3(4-1) = x 2 But f(x) y f"(f(x) =...