Solution to Let f be the function from x ={0, 1, 2, 3, 4, 5} to X … - Sikademy
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Archangel Macsika

Let f be the function from x ={0, 1, 2, 3, 4, 5} to X defined by f(x) = 4x mod 6. Write f as a set of ordered pairs and draw the arrow diagram of f . Is f one-to-one? Is f onto?

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It is given that x=\{0,1,2,3,4,5\}.

f(0)=4(0)\mod 6=0

f(1)=4(1)\mod 6=4

f(2)=4(2)\mod 6=2

f(3)=4(3)\mod 6=0

f(4)=4(4)\mod 6=4

f(5)=4(5)\mod 6=2

The given function as the set of ordered pairs

f = \{(0,0), (1,4), (2,2), (3,0), (4,4), (5,2)\}

Picture below represents arrow diagram of f

The function is called one-to-one if each x from the domain has exactly one image in the range, and no y in the range is image of more than one x from the domain. As we can see, is the image of both and 3, so the function is not one-to-one.

The function is called onto if every y in the range is the image of at least one x from the domain. As we can see from diagram above, this function is onto.

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Question ID: mtid-5-stid-8-sqid-1232-qpid-970