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.

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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

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