Question #258073

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?


1
Expert's answer
2021-10-29T03:02:08-0400

It is given that x={0,1,2,3,4,5}.x=\{0,1,2,3,4,5\}.


f(0)=4(0)mod6=0f(0)=4(0)\mod 6=0

f(1)=4(1)mod6=4f(1)=4(1)\mod 6=4

f(2)=4(2)mod6=2f(2)=4(2)\mod 6=2

f(3)=4(3)mod6=0f(3)=4(3)\mod 6=0

f(4)=4(4)mod6=4f(4)=4(4)\mod 6=4

f(5)=4(5)mod6=2f(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)}f = \{(0,0), (1,4), (2,2), (3,0), (4,4), (5,2)\}

Picture below represents arrow diagram of ff



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

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



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