WebDefine \( g: \mathbb{R} \rightarrow \mathbb{R} \) by \( g(x)=x^{2} \). Determine whether \( g \) is onto or one-to-one with an explanation. Show transcribed image text. Expert Answer. Who are the experts? Experts are tested by Chegg as specialists in their subject area. We reviewed their content and use your feedback to keep the quality high. WebMay 16, 2015 · Prove/disprove whether the following function (with inputs/outputs of real numbers) is injective and/or surjective: Using this helpful answer, I solved for. Therefore, is injective. Again, following that helpful answer, solve for , and then plug into : Now, plug into , and check if result equals , which would prove the surjective property.
Did you know?
Web1. f : Z → Z, f(x) = 2x+1. 2. f : R → R, f(x) = 2x+1. 3. f : Z×Z → Z, f(x,y) = 2x2 +y. 4. f : Z×Z∗ → Q, f(x,y) = x/y. 5. f : N → N × {0,1,2}, f(x) = (bx/3c,x − 3 · bx/3c), where bxc = greatest integer less than or equal to x. Solution: 1. One-to-one. It is not onto because the image contains only odd integers. 2.
WebOnto function is a function f that maps an element x to every element y. That means, for every y, there is an x such that f (x) = y. Onto Function is also called surjective function. The concept of onto function is very … Web(a) f is one-to-one iff ∀x,y ∈ A, if f(x) = f(y) then x = y. (b) f is onto B iff ∀w ∈ B, ∃x ∈ A such that f(x) = w. (c) f is not one-to-one iff ∃x,y ∈ A such that f(x) = f(y) but x 6= y. (d) f is not onto B iff ∃w ∈ B such that ∀x ∈ A, f(x) 6= w. 2. For each of the following, give an example of sets A, B and C and ...
WebApr 14, 2024 · Remember When I Wanted To Put Some PBS Kids Stuff Onto My Channel? Well I Couldn't Do It At First But Now I Can But To Give You The Truth, I'm Not Doing … WebSolution Verified by Toppr Correct option is B) Given, f:R→R,f(x)=x∣x∣ Redefined the function, f(x)=⎩⎪⎪⎨⎪⎪⎧−x 2,0,x 2, x<0x=0x>0 The graph of f(x) shows that it is a bijective (one-one-onto) function. Video Explanation Solve any question of Relations and Functions with:- Patterns of problems > Was this answer helpful? 0 0 Similar questions
WebMar 30, 2024 · Ex 1.2, 2 Check the injectivity and surjectivity of the following functions: (i) f: N → N given by f (x) = x2 f (x) = x2 Checking one-one (injective) f (x1) = (x1)2 f (x2) = (x2)2 Putting f (x1) = f (x2) ⇒ (x1)2 = (x2)2 ⇒ x1 = x2 or x1 = –x2 Rough One-one Steps: 1. Calculate f (x1) 2. Calculate f (x2) 3.
WebLet A = {1, 5, 8, 9) and B {2, 4} And f={(1, 2), (5, 4), (8, 2), (9, 4)}. Then prove f is a onto function. Solution: From the question itself we get, A={1, 5, 8, 9) B{2, 4} & f={(1, 2), (5, 4), (8, 2), (9, 4)} So, all the element on B has … marco cottarelliWebCorrect option is A) We have f:R→R,f(x)=cosx Let f(x 1)=f(x 2) ⇒cosx 1=cosx 2 ⇒x 1=2nπ±x 2,n∈Z Above equation has infinite solutions for x 1and x 2. Thus f(x) is many one function Also range of cosx is [−1,1], which is subset is given co-domain R. Hence function is not onto. Solve any question of Relations and Functions with:- Patterns of problems csrb applicationWebOct 12, 2024 · To prove a function f is surjective (onto), you must show that given any element y in the codomain, you can produce an element x in the domain such that f ( x) … csr banca d\\u0027italiaWebMar 30, 2024 · Consider the function f: A → B defined by f (x) = ( (x − 2)/ (x − 3)) Is f one-one and onto? Justify your answer. f (x) = ( (x − 2)/ (x − 3)) Check one-one f (x1) = ( (x"1 " − 2)/ (x"1" − 3)) f (x2) = ( (x"2 " − 2)/ (x"2" − 3)) Putting f (x1) = f (x2) ( (x"1 " − 2)/ (x"1" − 3)) = ( (x"2 " − 2)/ (x"2" − 3)) Rough One-one Steps: 1. marco cottone soccerWebTo show that a function f is not 1-to-1, it suffices to find x 1, x 2 in the domain of f such that x 1 ≠ x 2, but f ( x 1) = f ( x 2). If you want to show that a function f is onto, then for any y in the image/range of f, you must find x in the domain such that f ( x) = y. csra virginia addressWebGive an example of a function which is neither one-one nor onto. Hard. View solution. >. The function f:A→B given by f(x)=x,x∈A, is one to one but not onto. Then; Medium. marco cottage pieWebQ: for the data 2 5 7 X y 3 -3 3 find the value of y at X = 2.5 using: Lagrange Interpolation. @ newton… A: Note: As per the guidelines we are supposed to answer only 3 subparts. Please repost and write… marco countertop ecoboiler 20l