A duty f: A -> B is referred to as an onto function if the variety of f is B. In other words, if each b ∈ B there exists at least one a ∈ A together that.

You are watching: How to tell if a function is onto

f(a) = b, climate f is an on-to function. One onto function is likewise called surjective function.Let A = a1, a2, a3 and also B = b1, b 2 climate f : A -> B. ## Examples on top top function

Example 1:
Let A = 1, 2, 3, B = 4, 5 and let f = (1, 4), (2, 5), (3, 5). Display that f is one surjective function from A right into B.Solution: Domain = 1, 2, 3 = ARange = 4, 5The aspect from A, 2 and also 3 has actually same range 5.So f : A -> B is an onto function.Example 2: State whether the given duty is on-to or not.f : R -> R characterized by f(x) = 1 + x2.Solution: f(x) = 1 + x 2Let x = 1f(1) = 1 + 1 2f(1) = 1 + 1f(1) = 2 ----(equation 1)Now, permit x = -1f(-1) = 1+ (-1) 2= 1 + 1f(-1) = 2 -----(equation 2)but 1 ≠ -1∴ f is no one come one function.If f is onto climate O ∈ Rf(x) = 0there4; 1 + x2 = 0there4; x2 = -1x = ± √-1but x ∈ R∴ f is not on-to functionExample 3: determine which the the following functions f : R -> R are onto i. F(x) = x + 1Solution: f(x) = x + 1x = 1 ; f(x) = 1 + 1f(1) = 2x = -1 ; f(-1) = -1 + 1f(-1) = 0x = 0; f(x) = x + 1f(0) = 0 + 1f(0) = 1From the above we have the right to see the domain = -1, 0, 1 andrange = 2, 0, 1So, the given function is on-to.ii) f(x) = |x| + xSolution: f(x) = |x| + xFor x = 0 ; f(0) = 0For x = -1; f(-1) = |-1| + 1= 1 + 1f(-1) = 2for x = 1; f(1) = |1| + 1= 1 + 1f(1) = 2Domain = 0, -1, 1.Range = 0, 2, 2. So, the given duty is no on-to.11th grade mathFrom onto function to residence page

Covid-19 has actually led the human being to go v a phenomenal change .E-learning is the future today.Stay house , continue to be Safe and keep learning!!!

Covid-19 has affected physical interactions in between people.

See more: Palpatine:" Everything Is Proceeding As I Have Foreseen : How To Make

Don\"t permit it influence your learning. report this ad report this ad    report this adSite mapGMATGRE1st Grade2nd Grade3rd Grade4th Grade5th Grade6th Grade7th class math8th grade math9th great math10th great math11th great math12th class mathPrecalculusWorksheetsChapter wise TestMCQ\"sMath DictionaryGraph DictionaryMultiplicative tablesMath TeasersNTSEChinese NumbersCBSE Sample Papers